You should maybe read some articles about modern situations where people dodged conscription before assuming what is practical today. The average person who hasn't thought about it for a week is certainly in trouble but..
I'm not sure about that. Maybe? But... Firstly, there are surprisingly many people who are insanely patriotic so would volunteer anyway (perhaps fewer than in the past but perhaps still enough; see point three). Secondly, there are surprisingly many people who enjoy violence and killing people so would volunteer anyway (this probably hasn't changed). Thirdly, modern warfare doesn't need large numbers of people (this has definitely changed over time). And fourthly, a lot of modern people rather object to being ordered around by the government (I think this has probably increased a bit, at least; I can imagine that there are even people who would volunteer for military service when it's optional but would resist being conscripted).
In fact I cant disagree with most of what you've said, except to say that I was thinking from the state perspective, rather than the cannon-fodder.
Conscription has never been popular, and I think today in healthy industrialised nations it would be an exceptionally hard sell. Ukraine, Russia and (somewhat) Israel give us hints here of what might happen if the US or Germany or India started drafting all able-bodied young men.
It would be a disaster, but my guess is that it wouldn't stop governments from trying.
