There hasn't been a draft in most of our lifetimes. There also hasn't been a virus as deadly as this one.
So, maybe the better frame of reference would be: nationally mandatory vaccinations can be alright and make sense, under the same argument that allows the draft to be alright and make sense; we just need some quantitative framework under which it can be instituted.
For example: if covid becomes endemic (which seems to be likely), and we institute mandatory vaccinations for it during this phase of the pandemic, pre-endemic; the argument for mandatory vaccinations may make sense today, given the level of infections and deaths that are occurring, but will "mandatory boosters" make sense in three years when the level of deaths is (hopefully) far lower and more in-line with the seasonal flu?
The critical difference between a draft and mandatory vaccinations is: most people understand the general need for, but also hate the implementation of, the draft. Its a duty; its not desirable. In a democracy, this, alongside the massive cost and logistics effort of maintaining such a large army, acts as a very natural counter-balance to the impetus for people in power to abuse it.
Vaccines do not have such a counterbalance. They're very cheap per-shot, relative to the draft. The logistics are already in place and have successfully operated at scale. And, most concerning; many people want mandatory vaccination. No one should want it. Its an ugly necessity, but far too many people don't see the ugliness.
If you're reading this and need help to see the ugliness: Our government experiences corruption, like any government. Moderna's stock value has gone up by ~2,000% since the beginning of the pandemic. This, alone, is an obscenely powerful bias for people in key positions of power to push for more vaccination, irrespective of their need or efficacy; for example, maybe you assemble a panel of experts, who tell you vaccine boosters aren't necessary, then overrule the panel and say they're necessary anyway [1].
[1] https://www.nytimes.com/2021/09/24/world/covid-boosters-vacc...