I'm against this.
One problem with violence in the world is people who do it for reasons other than self-defense.
This can be state-compelled, it can be poverty-compelled or mercenary - it all boils down to an army of people possibly used to kill innocents for corrupt interests.
We need less military of a mercenary nature. We already have plenty of people who join for mercenary reasons (educational assistance! job skills!) mixed in with those who simply assume that the government can morally authorize killing so they don't need to worry about the moral issues.
This is in contrast to a WWII situation where people are specifically trying to oppose a threat.
This results in missions that can often be quite questionable - Vietnam being an example as we killed 2 million people for misguided reasons.
(Ask how the US could have a military occupation, and people often say, 'the US military would not do that, they're patriots who would refuse to subjugate the people for a tyrant'. OK - that's why it would likely be a foreign mercenary force, who care little for the freedoms of Americans they might largely resent. It's not likely, but if it DID happen, such a force makes a lot of sense - initially deployed for 'security'.)
This policy would create many more soldiers who just 'do as they're told' for the carrot of citizenship serving missions right or wrong.
If we needed that for legitimate defense, ok; we don't. We're an empire already and we need not to give our leaders the temptation of massive forces ready to use.
I'd support practically the opposite of this policy - almost anything but military service to earn citizenship (including the Peace Corps).
Unfortunately, a lot of people just get misty eyed at the word 'service' in the military and think this is a great idea. Our heroes!
I'm, not taking anything away from the very real sacrifices they make - but noting the dangers of misuse by politicians - including the harm to innocents abroad who don't get a vote, and get far too little concern from US citizens who do vote and often place the importance of the emotional gratification of feeling 'strong' above the lives of the all too invisible victims, to serve, usually, some big money interests.
This is a horrible policy. Stick to the military needing recruit citizens, the more they join for reasons of actual defense - including if the military has a hard time recruiting for missions that are far different than defense, that's a good thing - we do not need more mercenary forces out to serve any agenda the powers want, including, quite possibly, killing people somewhere who are fighting for their freedom.