Well, the genesis of feudalism is also the result of the post-Carolingian collapse, in what scholars called the "Feudal Revolution". It's not so much as western states moved away from Roman administration roots as much as the end of Carolingian empire meant local power is more concentrated in a period of fragmentation.
This in a way is similar to that of China when their central dynastic administration collapse and rules comes into the hands of local rulers. And power even in western Europe gets recentralised again once more by the 13th century. So it's not like Western Europe was always feudal, and even Anglo-Saxon England has a strong degree of centralised admin than the later Normans.
AFAIK, most modern scholars tend to avoid the term "feudalism" to start with, as it is a term with no clear meaning, and the most common one ("land held in exchange for oathsworn service") doesn't generally describe most European landholding arrangements of the time.
But that doesn't change the fact that, in-game, basically all of Catholic Europe is given a single government form (called "feudal"), which is strictly inferior to the Byzantine one.
The ability to draw upon a large population and actually deploy them is one that requires a degree of organisation, and via that a form of administration to get large armies mobilised and deployed to further regions.
Absolutely it does. Which is why the current system (where feudals get more levies, but Byzantines get more MAAs) is exactly backwards.
Because the lack of central administration meant that western realms tended to rely on smaller, but more experienced armies (as the various retinues tended to double as essentially muscle for the local lords, who would then take those retainers with them when called for service).
There's a reason that basically everybody (Greek, Frank, or Turk) tended to consider Frankish troops to be of higher quality on a per capita basis than Greek troops in a normal fight (to the point where Byzantines regularly relied on Frankish mercenaries, even during the Nicaean period when they had just lost the capital to Frankish crusaders): because they had plenty of practical experience in local skirmishes (and also tournaments, which tended to have direct military applications as well).
Even the Crusaders during the 1st crusade depended heavily on Byzantine logistics to even arrive at the Holy lands ( not withstanding the times the crusaders decided to try and attack Byzantine cities).
For most of feudal Europe, they generally did not need to wage wars further away, nor do they need to mobilise military manpower for a prolonged period. But when they do, they quickly turned into a more centralised administrative force than relying on just feudal levies and vassals.
Sure. But the game doesn't make that distinction; it just calls all the Catholic realms "feudal," and has them rely on the ruler's personal MAAs, and then levies raised from their vassals. Which renders them weaker than the Byzantine armies, and obscures the very real military strengths of western realms.
Catholic countries, after all,
were able to fight extended wars away from their homelands at times, even if it wasn't their normal approach. The English spent most of the post-1066 period at war in France, Scotland, or both (with occasional excursions to conquer Wales and Ireland). The HRE frequently found itself involved in wars in Italy, the Balkans, Eastern Europe, or France (including Barbarossa basically swatting aside Byzantine opposition during the Third Crusade). Charles of Valois led a French army into Sicily, and a few decades later lost it to an Aragonese invasion. And so on.
The Byzantine system absolutely had strengths. So did the Western European systems. And the fact that, in-game, the Byzantine system is strictly better is a real problem for game balance, especially as the Byzantines are already crazy strong without that bonus (as demonstrated by pre-RtP Byzantium, which was already a monster).
