Even if barbarians focused all of their attention to the ERE and had them clobbered,the ERE will just keep coming back because they've got the money and soldiers.It's worthwhile to note that while the WRE's army completely disintegrated in this period,the ERE's army continued to remain strong and even expanded.It's believed that by the time of Justinian,the ERE had an army of over three hundred thousand soldiers.The united Roman Empire had an army of only four hundred thousand at its' height.You get the picture how important the east was in regards to taxes and manpower.
The WRE army mostly disintegrated in 408 CE because they alienated the barbarians they had become dependent on. Apparently the ERE didn't (but it was still defeatable; Stilicho had to bail it out and it was badly beaten in the 440s.) But the essential difference is that barbarians, in stages, deprived the WRE of land, population and money on a permanent basis. In theory, instead of going to Gaul, Britain, Spain and North Africa (and Italy), the barbarians could've gone from the balkans to Asia Minor, Syria and Egypt, in the process undermining the ERE. It just so happened the WRE was mainly targeted.
Pay in the army's pretty shit,so why should they fight?Unlike the republic and the principate, the army was no longer a glamorous job because the WRE can not pay the army well.
But the latter third century army was big enough and effective despite the lousy, debased coinage of the time.
As to your point about men cutting their thumbs,that happened in the ERE as well.It had a lot to do with the fact that once in the army,your descendants will have to be soldiers too.In the ERE however,it’s manpower for the army isn’t that much of an issue because it can afford to pay people well,unlike the WRE.
I don't know if conditions for troops in the ERE were any better. Anastasius, late fifth century, had to reform the army.
Another factor is that even if there are citizens willing to fight,they wouldn't have fought well either,compared to the early Roman armies.Unlike earlier periods,the Roman army was progressively remodeling itself to an army that engages mostly in skirmishes and not field battles.This kind of warfare relies much more on individual skill rather than group fighting skill,as per earlier periods.This meant that a soldier would have to train much longer periods, so it was much harder to train troops.
But there were field battles in the 440s and at other times. I think the problem was not with the concept of field battles but a lack of enough regular army troops for them especially after 408.
Places like Aquitaine were ceded precisely because it was completely depopulated.The Romans actually negotiated from a position of strength when they forced the Visigoths into taking Aquitaine in return for military service.
I assume you're referring to the resettlement of Visigoths there under Constantius c 418. But prior to then, around 407-9, the Vandals and others had been pushed down there by Constantius, and stayed a while, prior to entering Spain so they must've messed it up badly, well before the resettlement (the Roman population probably fled). The point is, Aquitaine wasn't necessarily representative of the empire or even just the WRE as a whole.
Large aristocrats still existed in the WRE and they generally avoided paying taxes and had private armies as well.
I think this was more of an effect rather than a cause of WRE decline. The central government couldn't do much anymore so why pay taxes and rely on it for defense?
If you want to blame anyone for the unwillingness to fight,you should probably blame them.It matters not whether the invaders outnumbered the local population or not because the percentage of people the empire can mobilize is always going to be smaller than what the barbarians can mobilize.The entire adult population of a barbarian tribe can be mobilized to fight whereas this is impossible for an entity like Rome.
But trained, professional Roman armies had long stymied barbarian encroachment, even in the third century when masses of them swarmed across the border.
The manpower pool has been depleted,and what remained of that is largely in the hands of the aristocrats.They are NEVER gonna yield their tenants to the army. Majorian got killed precisely for trying to combat this group.
IIRC the law tying peasants to the land had existed since the time of Diocletian yet Roman armies remained big for decades after that. Note that sons of soldiers had to serve but while this in theory should've just about sufficed, it obviously didn't work out...I don't think soldiers stopped having sons. The latter just wouldn't fight--Martin being an example.
Most commoners don't give a damn about the good of the public. The empire has always either built up the army through incentives or physical force. The army was conscripting people after the mid-third century,that's why they managed to keep the army manned.That didn't work anymore because the manpower pool completely dried up.
I don't think it did in the sense of manpower literally not being there anymore. Most citizens just would not serve anymore. Christianity probably had much to do with it. I read in LATE ROMAN INFANTRYMAN that recruits had to be locked up nightly while being transported to their bases. Faced with citizen unwillingness the empire finally just gave up and hired barbarians instead--but ultimately alienated most of them in 408.