The Romans had so many technological and tactical advantages over other civilizations. For instance, packing the infantry tight together and pressing into the enemy proved far superior to the individual no-strategy-charge employed by barbarians. However, not 400 years after the fall of the Western Roman Empire, the Vikings are back at it again charging in like maniacs and the West Franks are using long swords. Similarly, the segmented armor which was so much more effective and deflecting and displacing blows than mail was soon replaced by mail soon after the Roman's disappearance from Western Europe. Why did nobody emulate them?
Well, from what I'm reading in the follow up to your questions the answer is rather simple: economics and organization. For the rest of my explanation I will assume we are talking about the Western Romans, since the Eastern Romans kept the Roman ways for a long time after the fall of the West, so please, in the follow up "Roman" means "West Roman".
It was far more expensive to fight like the Romans than to fight like the Franks or Vikings. Of course, if we look back on it and apply our modern interpretation of the state to those you mentioned, it seems like their leaders were daff not to fight like the Romans. The problem is that the Romans were a far more organized and centralized state than any that would follow for a long while. The Romans could organize the formal training, the standardized equipment and the formal structure needed to field a Roman style army. None of the powers in the West could. Their traditions mostly devolved centralized leadership into feudalism. The state, such as it was, was no longer in charge of arming the armies or even maintaining a formal standing army in most cases. The armed forces of the day were called upon by the liege lord down and they were a formal responsibility of the vassals. All of the successor kingdoms were primordial feudal holdings, they still depended on the Roman tradition to legitimize their rule but as Rome declined, they would move towards feudalism.
The Roman way of fighting was abandoned because nobody around after the fall of Rome could maintain it. There is very little incentive for a vassal to train his troops as the Romans would have and he may not have the means to arm them anyways. Instead, you knight a bunch of men, give them a responsibility to keep arms in exchange for a formal place in the power structure, you make up the bulk of your armed forces with peasant levies, and, perhaps, if you are wealthy, men-at-arms (give them the name you will depending on kingdom, but, everyone had men-at-arms) or mercenaries and you have an army. Knights would bring a few men to the field, Barons would bring a few knights and some men, Counts would bring a few Barons and some men, Dukes would bring a few Barons and Kings would bring a few Dukes. You drew your armed forces from the people directly below you on the vassalage chain, instead of holding on to standing armies. Then they'd all meet on a field somewhere and bash the peasants heads in or fight in single combat, whether on the battlefield or off.
I'm quite sure the King would have loved to have a Roman styled army at his beck and call but his power depended on the allegiance of his vassals and the allegiance of his vassals depended largely on their own prestige and full coffers. That means you want to field as many men on the farms as possible in any case, so, you don't want them training to become legionaries. You have your knights for that.
So, in short, none of the successor kingdoms fought like Romans because they couldn't afford it in men, equipment or organization. Then, over time, with improvements to equipment and changes in tactics, the Roman ways became obsolete. So, by the time you have a state with strong enough institutions to support a professional army, such as they were in Roman times, you couldn't fight like a Roman.
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You might want to rethink your image of the 'vikings charging in like maniacs,' as when the early medieval Scandinavians went to war (i.e. when they weren't going a-viking) they fought in fylkingar, or formations. Konnungs skuggsjá, Heimskringla, Sverris saga konnungs, Egils saga, and numerous other texts all relate how medieval Scandinavians and British (in the case of Egils saga) fought large-scale battles in formation.
Reckless charges were for viking raids and duels, rather than actual battles.
The Roman system was highly dependent on the organization of the Roman state, as has already been covered in another answer. However, I would like to correct a misconception on your post. The Romans didn't bunch together to attack. In fact, this is part of the reason they suffered one of their top military defeats at the Battle of Cannae. They actually avoided doing this.
They dropped the phalanx, which actually does work by bunching together and pressing into the enemy (and making sure you didn't get flanked). They adopted the maniple system, which was more maneuverable, had open spaces and allowed men to switch in and out of the front lines to keep the front line fighters as fresh as possible. They would change this model later on later on, but the idea of maneuverability remained. Lastly, the short sword called the gladius was integral to this fighting system, as it allowed them to stab past their upheld shield, which was holding back the enemy.
This all speaks to the importance that the Roman state provided, as drilling and training a professional (paid and standing) army requires a good organizational structure to pull of.
For instance, packing the infantry tight together and pressing into the enemy proved far superior to the individual no-strategy-charge employed by barbarians.
There are erros in your question. Thile the romans did fight together, they wher not tight as far as military formations go, exept during a siege or when fighing horse archers.
Next, barbarians, what kind of barbarians are you talking about? The Huns did not just charge. Many of the later germanic tribes fought more like the romans then the first germanic tribes (Cimbri).
However, not 400 years after the fall of the Western Roman Empire, the Vikings are back at it again charging in like maniacs
You have seen to many movies. Vikings did not charge, they actually build little defencable castles, raided and when attacked build shieldwalls.
and the West Franks are using long swords.
The late roman empire when more and more away from the gladius (short sword) for longer swords. Partly to fight germanic tribes partly because germans join the legion.
And the vikings where using long swords as well.
Why did nobody emulate them?
First of all they where emulating the barbarians long befor the end of the empire. Second, if you look at east rome you see a change in armor and organisation as well. The reality is warfare change, the challanges that the faces changed and thus armys changed.
In France and Germany you hade a ruling warrior class that dominated by having a horse, armor and castle. Most of the time they where not fighting battles they where fighting farmers. When a lord would gather his levys to attack somebody they did not have the money to equip them roman style. They did not have the training to fight roman style.
Most of the time the romans where sitting and fortifitcation systems and not moving around to raid one castle or give some farmers a beatdown.
If you look into the eastern empires you will also see more cavalery, specially horse archers and also some changes in infantery.
Oh boy am I going to have some fun.
However, not 400 years after the fall of the Western Roman Empire, the Vikings are back at it again charging in like maniacs and the West Franks are using long swords.
no, no ,no. They used shield walls of their own, ESPECIALLY the vikings. In fact an early meideval shield wall would be more tightly packed than a roman manipular. So did the saxons, the franks, and the new Italian occupiers. Only a nobleman would be using a long sword and he would have a short sword to do his killing in the shield wall anyway.
Similarly, the segmented armor which was so much more effective and deflecting and displacing blows than mail was soon replaced by mail soon after the Roman's disappearance from Western Europe.
Most Roman Legionnaires used lorica hamata, ESPECIALLY, in the late imperial age. Lorica hamata was mail. And chainmail especially the more advanced type they used in the low medieval period was easily as effective as lorica segmentum. Plus it is much much cheaper.