Allowing a small country like Luxembourg to have military (but not political or industrial) control over a country like the USA sounds like a great exercise for a....simulation. Which is exactly what PI has always said that HOI is intended to be.
HoI is not a simulation and I'm pretty sure we have never said it was. It's merely a game
Anyway, capturing equipment is interesting, but you certainly shouldn't get the entire remaining OOB. Defeated nations tend to be a bit upset and try to scuttle/destroy/disband their units rather than let whoever just stomped them use them for themselves (their former allies might "help" there too). And then there's the fact we don't model things like ammo and replacement parts. It's all very well capturing a stock of enemy guns, but if they use a different size of bullet they're only useful while captured ammo lasts, and it complicates supply...In the end it just made more sense to give Germany a little more IC so they could build an extra division rather than equip one from captured equipment.