I'm mostly going to talk about Wales because i don't feel qualified to talk much on Irish history.

Well Wales was briefly united entirely at one point under Gruffydd ap Llywelyn and under Rhodri Mawr the majority of Wales came under his rule. The problem for Wales in a permanent union was the Welsh inheretance system had a ruler split at least a part of their land between their sons. As such if a one of the kings came to rule multiple of the Welsh Kingdoms during their life they would usually split these up again between their living sons upon their death. Which only worked for as long as the sons could get on with each other which often wasn't very long.

Another major aspect is in of itself the England beating them down thing. English kings tended to view an overly united Wales as a possible threat to their ability to control the Welsh, and so Wales' much larger neighbour would often if it were able specifically step in and attempt to prevent such a thing. Welsh Kings with ambitions to rule all of Wales tended to be most successful when English attention was divided, for example Gruffydd came to power during the point when Danish rule in England under Harthacnut, son of Cnut the Great was weak in the 1039. Later when he began his period of unification, expanding southwards England was back under English control under Edward the Confessor but he was juggling the problem of the fact he had to contend with the ambitions of the powerful Godwin family and wasn't a particularly aggressive ruler in many ways. Grufydd was able therefore to find Saxon allies among nobles who were enemies of Harold Godwinson during the 1050s which gave him friends in the English court who could dissuade Edward the Confessor from letting Harold off his leash for a short while. This never lasted and in an even match up the size difference between the two countries meant that once Edward allowed them to the Godwinson's military power suppressed anything the much smaller Welsh kingdom could achieve. With Gruffydd dying in the conflict Harold ensured that Gruffydd's kingdom would be re-divided into its smaller constituency.

The other thing that doesn't help is the geography of Wales means much traveling between different parts of Wales can be fairly difficult. That means that sending an army from one end of the country to another takes time and requires a fair bit of effort, even simply sending messages could be slow in the bad weather conditions. While this meant that Wales' total conquest by England was a slow process and even after it regular rebellions flowered again on occasion despite their relative sizes but it also meant it was difficult for a single Welsh King to conquer the other kingdoms and effectively rule the entirety of Wales.

As u/the_direful_spring rightly points out in the case of Wales, the lack of primogeniture inheritance laws was certainly a constant barrier to consolidation of lands under one ruler. A lack of easy communication also exacerbated existing ethnic, linguistic and cultural differences inherited from different Celtic tribes and disparate levels of Romanisation, the exact nature of which remains poorly understood. The common factors, which arguably by the later dark ages included some variation of Brythonic Welsh and Christianity, were insufficient to provoke spontaneous unification against a back drop of strong local power bases and the vested interests of different 'royal' houses. The mountainous geography of Wales, moreover, even to the present day, frustrates easy latitudinal communication between North and South, and Wales has long had better communications with neighbouring regions of England than it has within Wales itself.

However, it is worth noting that politically speaking England was not all that different, from what we know, following Roman withdrawal up until the ninth century, in terms of having multiple petty kingdoms. It was only with the rise in fortunes of Wessex under Alfred the Great that a proto-England began to be seen, and even then it was by no means homogenous or consistent for some time. One of the reasons English history starts in 1066 is partly simplicity, as it is really only after this point that a Kingdom of England, with a geographically familiar whole entirely separate from Scandinavian politics definitively emerges.

Therein, for Wales at least, I think lies the answer to the question. As England emerged, it expanded pretty quickly into those parts of Wales which were accessible to it. South eastern Welsh kingdoms such as Morgannwg, Glwysing and Gwent at various times became conflated with the landowning families and dynasties of neighbouring English counties, which would eventually evolve into the Marcher lordships under the Normans. While there were native ruling families in these areas, a mixture of conquest and intermarriage meant that much of the flat, arable and accessible areas of Wales formed a part of the political system of England, which afforded lordships such as Glamorgan, centred on Cardiff, far more trade and political opportunities that would pursuing an independent Welsh kingdom.

Those parts of Wales which preserved independence did indeed push, at various times, to resist English encroachment and establish a more Cymrocentric nationhood, the most famous examples perhaps being Llewellyn ap Gruffydd, Llewellyn Bren and Owain Glyndŵr. However, all came from regional royal houses and commanded little support in the southern coastal plains which had risen in commercial and political significance. Considering the disparity of numbers then, not only between England vs Wales but in this case England and South Eastern Wales vs the rest of Wales, it is unsurprising that such efforts were ultimately failures. Subsequent centuries saw far more successful efforts on the part of the Welsh to establish a British narrative which allowed them to be included more formally in the Kingdom of England, culminating with the Acts of Union which brought the Welsh counties entirely in line with the English legally.

TLDR In the case of Wales, a mixture of numerical disadvantage, political expedience, and a lack of a galvanising homogenous identity meant it was always too intertwined with the emergence of England to be a entirely separate political entity from it.