You are entirely right : it seems strange that Europe would have "rebooted" instead of continuing on the same lines and structures of the Late Roman Empire. Unsurprisingly, it didn't happen, and Barbarian kingdoms are largely post-imperial Roman states.

While more (much more) can be said, I proposed some answers that might interest you.

- How did the medieval Western European states utilise Roman institutions and their legacy? ; u/Libertat

- What happened to the former Roman aristocracy in Western Rome after its decline? ; u/Libertat

Barbarians, as political entities, weren't tribes in the anthropological sense of geographically and genealogically defined groups, but political ensembles defined by their relations to the Roman state, having some dual identity with a distinct leadership and citizenship but being largely a Roman militarized community or army. In this sense, the difference between a Roman warlord as Syagrius and a Barbarian warlord as Clovis was meager : with centuries of creolization and integration of Barbarian leagues as they appeared in the IIIrd from elements already present along the limes since the Ist AD, newcomers attracted by the opportunities; and deserter, fiscal refugees or Roman slaves; we can't consider Barbarians as suddenly mass-migrating from their primeval lands.

Not only new rulers didn't began from scratch, but they weren't necessarily "new" rulers and rather peoples and leadership already integrated within Roman institutions and taking over entire regions from there.Note that the situation in post-imperial Britain and Danubian regions is quite different, giving the political collapse there was accompanied by a societal collapse : newcomers settled in a ruined peripheral region and often were people not in direct contact with the Roman state (which doesn't mean they ignored old structures, just that these didn't necessarily formed the first basis of their new societies)

I'd want to develop a bit on your point about Motte-and-baileys : these are not a product of Barbarian kingdoms, but appears only in a period of general political and military insecurity in the Xth century, as the Carolingian empire collapsed and as Viking, Saracen and Hungarians raids continuously threatened not only the periphery. While the Vth century is a period of certain economic decline in western Romania, the political transition was much smoother inspite of the aggressive constitution of post-imperial states by Wisigoths, Vandals or Franks; especially comparatively to the general insecurity of the IIIrd century with endless civil wars and raiding which led Roman cities, but as well rural demesnes, to be quickly fortified.

For most of the early medieval period, there's not a widespread concept of private fortification or of local elites taking over public power : Barbarians would mostly maintain public fortifications built in the Late Empire, more uncommonly built new ones (as the new fortifications of Ostrogothic Marseille, on the Eastern Roman model).In relatively peaceful regions such as most of Merovingian Gaul, some castra (being understood there as fortified secondary agglomerations without being an institutional seat) didn't even saw the reconstruction of damaged walls for centuries : until the mid-IXth century, there's the idea that in the absence of a real threat, walls could be left in disrepair or even partly demolished to make room for new constructions.

It doesn't mean, however, that there wasn't a confusion between public and private interests : semi-public castra were equally widespread, the constitution of hill-forts or fortifications in plains centered on a particular feature (church, monastery, villa, etc.) thus demonstrating the dominance of a family or power on the region; without being stronghold or purely private establishment.

When Frankish influence on the right bank of the Rhine began to be felt, instead of a delegation to local principalities, it often took the form of founding (or re-founding) agglomerations such as Frankfurt.

There was the idea of non-urban fortification, still : the borders regions between Carolingian-era Franks and Saxons, Danes or Wendes were defended by a set of fortifications manned by local peoples (more or less closely related to the peoples they were defending the realm against) considered as allies and federates. These forts were essentially protected by earth and timber walls, arguably because their function wasn't to be strongholds but to control the region and its exchanges.

Noble housing wasn't really much fortified in the period : either urban monuments such as repurposed baths; either, for the most part, rural villae; they could host a military presence but were essentially protected by a wooden palisade. Eventually a Frankish of Gothic palace of the VIIth century would have been essentially familiar to a Roman noble or landlord of the IVth century, with significant changes in matter of decorum and display.

How did Anglo-Saxons burhs become towns have a fantastic answer by u/BRIstoneman which covers their defensive and urban make-up if you're interested on insular fortifications development.

- Civilization versus Barbarians? Fortification Techniques and Politics in Carolingian and Ottonian Borderlands; Joachim Henning; 2005

- De la cité Arverne au diocèse de Clermont : Topographie ecclésiale, fortifications et peuplements de l’Auvergneentre Antiquité tardive et haut Moyen Âge (Ve-Xesiècles) : une approche archéologique; Damien Martinez; 2017

- Les résidences des élites et les fortifications du haut Moyen Âge en France et en Belgique dans leur cadre européen : aperçu historiographique (1955-2005); Luc Bourgeois; 2006

First off, it's very important to keep in mind that the extreme territorial fragmentation and political decentralization often associated with "medieval Europe" did not immediately emerge after the collapse of the Western Roman Empire. Rather, this was a phenomenon of the post-Carolingian collapse, and was largely restricted to what is now France, Germany, and the Low Countries. For example, you mention the "motte-and-bailey" castle as one of the characteristics of a fragmented political order, and you would be right with that identification. However, motte-and-baileys only emerge in the 10th century in areas like northern France, as a means of protection from Viking raids. The weakness of the later Carolingian administration essentially forced local lords to take matters into their own hand and provide protection for their lands and subjects, which the "central" government was unable to provide. Widespread castellization was a phenomenon of the High Middle Ages rather than the Early Middle Ages, and had nothing to do with the initial Germanic migrations into the Roman Empire.

Broadly speaking, we can use the following schema to describe the evolution of political order in Western Europe in the Middle Ages:

Stage I: Collapse of Western Roman authority, accompanied by the migration of Germanic tribes into the Western Roman Empire.

Stage II: Establishment of new Germanic-ruled kingdoms in formerly Western Roman lands, such as the Merovingian kingdom in Gaul and the Visigothic kingdom in Iberia. Note that the internal administrations of these kingdoms still had considerable continuity with Roman precedents, and were not "built from scratch" (to use your words). In Gaul, for example, the old Roman senatorial elite continued to dominate the civil and ecclesiastical administrations under Merovingian rule, with the Franks simply ruling as a military aristocracy overlaid on pre-existing Roman institutions.

Stage III: Disintegration of the Western post-Roman early medieval order after the 9th century, which was facilitated and accelerated by the Viking raids and the economic disruption which they caused. It was during this stage that we see extreme territorial fragmentation and political decentralization, with practically every local count acting independently of his theoretical "feudal lords," and treating his domain as a de facto state of its own.

Why did the post-Carolingian collapse result in such a fragmented political order? That's a very complicated topic which is the subject of entire volumes, but the simplest answer I can give is that it was the outcome of Carolingian political economy. Generally speaking, one of the characteristics of the early medieval period in Western Europe was the decline of trade, monetization, and the market economy. The relative absence of such economic forces meant that not much money income actually flowed into the coffers of kings, even if they ruled a large and productive empire like that of Carolingian Western Europe. So given such an economic situation, how was the ruler of a kingdom to carry on the essential tasks of state and ensure the maintenance of military forces? The simplest and most effective way to do so would be to grant lands to subordinates, both to reward them for prior services rendered to the ruler, and to give them the economic base for rendering future services. Under Charlemagne, for instance, the Carolingian officials received a beneficium or fief - a tract of land to be held, if all went well, for life - in exchange for an oath of vassalage, and a promise to support his liege with military forces (to be maintained using the beneficium) when called upon. This personal bond of vassalage is what is often characterized to be the essential element of "feudalism." The agreement between lord and vassal was a contract, and if the vassal did not render his specified obligations, his beneficium could be revoked.

It's very important to point out that Charlemagne did carry out such arrangements because he was "forced" to do so by unruly, over-mighty subjects. He granted such benefices to his vassals because that was the most efficient way of utilizing the kingdom's resources, and ensuring that military forces could be cheaply and effectively maintained. The alternative would have been to construct a kind of highly centralized and bureaucratized system where all the produce of the land was somehow concentrated in Charlemagne's hands, and then distributed by a central bureaucracy to soldiers who were directly maintained by the king. Such a system would have been nightmarishly inefficient, and probably also impossible to implement given the available technology and resources (keep in mind the absence of the market economy which I mentioned earlier, as it was the market economy which enabled more centralized systems of military finance). So Charlemagne's decision to give away lands to his vassals should not be construed as an "erosion" or weakening of state power, but rather as an effective means of maintaining state power. It was very different from the case of the Norse chieftain Rollo demanding and receiving Normandy as a "fief" from the weak late Carolingian ruler Charles the Simple, in the year 911.

Likewise, it also important to point out that although the early medieval Western economy was more "primitive" and "rustic" compared to the Roman economy at its height (which boasted a huge money supply, extensive trade networks extending as far east as India and China, and an enormous diversity of goods and services for sale), the Western economy was by no means "unproductive." Agricultural production, in particular, did not decline over the course of the early Middle Ages, and Western European population indeed expanded considerably during this time, from an estimated 27 million in the year 700 to over 40 million by the 10th century (see Slicher van Bath, The Agrarian History of Western Europe). However, this population increase - and presumably, the corresponding economic increase - did not benefit the ruling kings as much as the various local lords, who had direct access to the agrarian economy and whose relative strength vis-a-vis the monarchy increased during this time period.

Thus, when the Carolingian empire began to collapse after the 9th century due to the combination of internal conflicts and external pressures, it was only natural that the political order would fragment into local lordships. It was the local lords who could provide security, and it was they who could raise and maintain armies. The later Carolingian kings were too weak to support their vassals and protect them from their enemies, and thus, they could not inspire loyalty from them and were discarded as largely unnecessary. In many cases, the local lords themselves fell victim to the disintegrating forces that had afflicted their liege, as they had alienated much of their lands to subordinate barons who subsequently became independent, and no longer needed support from their former liege. The region of Anjou in western France, to give one example, saw a great deal of territorial fragmentation during the reign of Count Fulk IV (r.1067-1109), to the extent that the Country had disintegrated into over 40 "mini-states" ruled by barons. Each of these mini-states was based around a castle and covered an area of about 25 sq. km., as that was the maximum area that a party of armed men could effectively patrol in a single day while returning to the castle by night fall. Such fragmentation was the result of the "central" authority (in this case, the Count of Anjou) having nothing to offer to his vassals, and also lacking the coercive means to punish them. What originally had happened with respect to the Carolingian kings and their direct vassals was now being mirrored at lower and more localized levels.

How was this disintegrative process stopped, and eventually reversed? The answer, as you might have guessed based by on my introduction, seems to be the return of the market economy. This is most easily visible in the case of Normandy, which was unique from other French principalities in that managed to largely avoid the extreme fragmentation that afflicted other areas, such as the aforementioned Anjou. Indeed, the Duchy of Normandy developed one of the most centralized and advanced administrations in Europe, and had a powerful military staffed by loyal vassals and officers. This military would later prove capable of conquering even a kingdom as large and rich as England. The secret to Norman stability and success seems to lie in the fact that Norman dukes had reliable and consistent access to a resource that other French lords lacked: money. Since the late 10th century, Normandy had emerged as a major commercial center as the entrepot of North Sea trade, and there was a significant amount of money in circulation here. The Duke of Normandy was able to tap into this commerce and collect a steady stream of money revenue from tolls and market dues, which was far more useful and profitable than the produce from the lord's demesne. This money revenue allowed the Duke of Normandy to continue the "generosity" towards vassals which the Carolingian kings and other French lords had been forced to abandon, since there is only so much land that you can alienate through land grants before you run out. Since the Norman dukes always had money available to distribute as rewards, their vassals remained loyal, and continued to serve their liege faithfully in the hope of obtaining such awards. In contrast, because the lords in other regions had little or nothing to offer to their vassals, it was only a matter of time before their ties of vassalage became strained.