As one of the Vietnam generation (as well as an actual, boots on the ground Vietnam veteran), I'll just add another consideration -- warm bodies. When the U.S. first contemplated the invasion of Iraq, the then-Chief of the JCS told the administration that post-invasion we would need 300,000 pairs of boots on the ground to sustain the situation once we were in control. The administration fired him and decided it could be done with fewer than half that number.
What we have in the whole region now is a result of that decision.
The problem is that we didn't have 300,000 pairs of combat and combat support boots to throw into Iraq. And we have no way of ramping up to get that many because neither party has the gumption to reinstitute the draft. The millennial generation isn't interested. We have spent too many years teaching successive generations that there is no personal responsibility. Whatever the problem, it's always someone else's responsibility. (Which, of course, is why APS keeps Fistful around.) When I was in high school and college, the draft was there and it was simply accepted as a fact of life. When someone was actually drafted, there was no "Not my President!" grade moaning and kvetching, it was just a general sense of resignation ("Oh, well -- I almost dodged it.") That attitude of "It's not my responsibility" has become so deeply ingrained that neither party wants to risk the certain firestorm that would follow if we started up the draft again. As far as I know, the draft still exists on paper, but I'll bet most 18-year old male children (if there are any left who don't self-identify as Caitlyn Jenner or a leprechaun or a fir tree) don't even bother to register, and have no fear of being punished for that because they know they won't.
Having a draft card was so much a requirement in my day that when I was released from active service we were advised to have a copy of our DD-214 reduced to wallet size so we could carry that to show if we were asked for our draft card. I did that. Carrying that became so habitual that I still have it in my wallet today.