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!
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.
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.
You say it's a bad idea, so it's a bad idea for an American citizen to join the armed forces too?
If we want to strengthen America (military & economy) immigration reform is needed! This could be unpopular but such reform could be ...those who want to come here must serve in our armed forces for x amount of years and can bring two to four family members here that are able to start working and contributing to the economy immediately (pay taxes). Rounding up and getting of rid of these eager want to be Americans when we have adversaries with larger armies and we bang the drum on beefing up defense (and our economy) doesn't make sense to me.