I like the idea of civic engagement / service in theory too, but I feel like the Vietnam war was a demonstration of possible failure modes when draft is in place: a lot of poor kids died, some rich kids allegedly used parental influence to dodge the draft. No incentive for leaders to avoid war while loop holes remain for their own interests.
Also the poor kids started killing the rich kids.
https://en.wikipedia.org/wiki/Fragging
A major reason why the draft was stopped is that because when you take a disunified and unwilling populace and start giving them weapons, their target may not be the enemy.
The word allegedly should be dropped many ie.. Taco got out of it, however much better men John McCain, John Kerry, and Robert Mueller did not. Serving is okay if everyone serves no exceptions.
People greatly overestimate the number of Vietnam vets who were drafted.
A formal declaration of war by Congress is the minimum.
Otherwise I agree that the incentives are warped.
I think you could argue the draft forced the war to be real for more families (and the expansion of TV), intensifying the resistance to it. Quick googling says almost 10% of the population served in Vietnam in some capacity. Less than 1% served in the War on Terror.
This was part of Charles Rangel's (D) reasoning to propose bringing back the draft. [1]
1: https://en.wikipedia.org/wiki/Universal_National_Service_Act