The traditional incentive that the military gives in these situations is that your spouse and children will be well taken care of if you serve, and even better taken care of if you die in service. Not endorsing that approach, just explaining.

Indeed, come here and expedite citizenship by serving America for an X number of years! In return along with expedited citizenship your partner and any kin can join you with your partner required to work/contribute some to the economy. Heck work in one of these new factories part or full time (if full time the new factories offer free day care).

Personally this concept is a more humane one then rounding/exiling want to be Americans in which the majority are not criminals! No they are hard workers coming here for a better life, why not give that to them and in return they "Make America Even Stronger!" ;-). That's what the current admin wants beef up defense, yet to me with immigration they are taking the wrong approach!

Both the Romans and the US had success with immigrants in the military, provided that they were thoroughly mixed. A unit with 35 ethnicities in it usually does not rebel "like one man".

The Roman way started to fail when they moved to the foederati model, where there would be units of, say, only Goths under a Gothic commander. That proved dangerous.

Did either work for Kakania/Austria-Hungary?

The Hapsburg empire, in its various incarnations, existed for almost four hundred years (1526-1918), and most of the time, their troops were loyal, so the answer is yes?

But one has to be careful: while their military was diverse, it wasn't really made of immigrants. It was simply built out of very diverse local ethnicities that were settled in the same place for centuries. Which means, for example, that when the Kaiser fought against the Turks, everyone involved regardless of language had an incentive to fight, because their own homes and freedom were at stake.

How many wars has American been in within the past 40 to 50 years?

You say it's a bad idea, so it's a bad idea for an American citizen to join the armed forces too?

The best army/weapon are those never needed to be utilized. Enemies won't pick up fights because your weapon/army are way stronger than theirs. Therefore we cannot regard army/weapon as "not used" or just wasted.

The French Foreign Legion is a famous counterexample to your argument here. They might actually have the best Esprit du Corps in the world. In particular because they have to since they are indeed comprised of random foreigners and historically at least low-level criminals.