Everything you are saying about Vietnam is true, but I feel like you are mischaracterizing the timing of draft and its enforcement. Elvis Presley was famously drafted during peacetime. The idea that we could maintain a fully staffed military with volunteers only, wasn’t seriously considered during this era.

What Vietnam did was contribute to killing the draft, although mandatory registration for selective service continued.

https://www.sss.gov/history-and-records/induction-statistics/

Notice that the pattern is pretty much, more people for war, fewer people for peacetime, and then it tapers off to the end of 1973, because Vietnam and the ensuing backlash and protest, exposed all of the worst problems with the draft