I can't speak specifically for the Navy, but as an Army officer I've been part of the pipeline that turns recruits into air traffic controllers, which is a pretty in-demand role. [I've also been part of the pipeline that turns college students into officers and pilots, but they don't go through "boot camp" in the same sense that enlisted members do.]

Your intuition is sort of correct, but sort of backwards. First, someone who qualifies for an in-demand role is less likely than most recruits to wash out because they are more qualified than the average recruit to begin with. Second, if someone fails along the way to becoming an air traffic controller or linguist or some other difficult job, there are a lot of other jobs that they can step down to and handle with ease. So we'd say, "Hey, you didn't make it, but this is a tough program so there's no shame in that, and here's another program that we can send you to do instead, if you want." On the other hand, if someone signs up to be a shower and laundry specialist (yes, that's a real job) and they fail in that program, we probably don't have much else that they'd qualify for, so they might be out of luck no matter how much they want to stay in uniform.

Edited to add: Of course, "boot camp" is "boot camp" for everyone, (mostly) regardless of the specialty that they signed up for. I'm mostly speaking above about the second stage of training.

These numbers are for enlisted recruits. To wash out of basic training/boot camp and be enlisted there has to be serious problems. Bed wetting, serious violence, egregious disciplinary problems or major integrity violations, Maybe being overweight or failing physical standards at the very beginning / end of training. With most of these things you just get rolled back and stay longer in training. The most common drops are early, often for integrity problems like lying to a recruiter about a criminal past or failing the initial drug test. After that if a person is kicked out of recruit training it's for the issues mentioned above and there doesn't seem to be any "fixing it"

These decisions are made by training commanders pretty much on a case by case basis, often with the armed service's needs in mind. Everyone who's at enlisted basic training is needed, because it's about volume.

I'll underscore this point. Basic training is not hard, and we really want people to pass. Like you said, if someone really wants to be there, we'll typically work with them for as long as necessary to get them through... second and third chances, for sure, with instructors practically holding their hand. Like I said in my other comment, if someone just couldn't handle tough academics, we found an easier job for them. When I actually separated people from the Army and sent them back to civilian life, it was usually a mutual decision.

No, I was a nuke coming into the navy, the hardest to recruit supposedly, and I was treated perhaps worse for it, but definitely no better. Boot camp is the same for all.

You could have a cs degree working in cyber security and they still make you do the same bootcamp. If you get in through college programs you do the same playing soldier in the woods at your local base once a month thing too. If you join the marines the hazing/bs you put up with is certainly worse both in bootcamp and in terms of the routine monthly drill.