You can train a draftee to be a cook, chip paint, or stand a deck watch all day. Those are not the skill areas we're lacking in. We don't need more BMs, CSs, or HMs, as reflected by those rates' legendarily paltry advancement rates. We do have programs for foreign nationals to gain citizenship, but the problem is that they're foreign nationals that can't get security clearances.
We need cryptologists, Aegis techs, EW techs, electronics techs, cyber warfare techs. Even with the best, most highly motivated high school graduates, those training schools and qualification pipelines take years and still have a high washout rate. Officers with fancy college degrees don't necessarily make it through. We talk a lot about nuke power school, but there's plenty of non-nuke schools that would give anyone a very hard time. And just like we have issues retaining nukes, we have just as much of a problem retaining those highly technical non-nuke ratings.
You can't draft someone off the street, give them six months of training, push them through school without rigid academic standards, put them in front of a signal processor, and expect that to go well. The problem is not just the number of bodies, and recruiters that cut corners with things like medical and background investigations are just wasting everyone's time...there are sailors that don't even make it to their first fleet command once the issue is caught.
If you want me to provide a solution, sure: 355-ship Navy is a pipe dream. The goal end strength is unachievable unless someone starts paying E5s as much as O1s. Build capacity and capability by means other than sheer numbers.
There is manpower and resource cost associated with taking in manpower, draftee or not. If we don't do it carefully and deliberately, we are wasting everyone's time. Recruiters can push high school kids off their desks, but if they're not meeting the Fleet's needs, they're just pushing a problem to someone at boot camp, or 'A' school, or a ship/squadron somewhere. And that is much, much worse.