Per OPNAVIST 1420.1B, there's 170 allowed slots under the SECNAV nomination, from what I've heard from these forums and my DH is that generally every year there are unfilled slots. For ex. there were only 59 prior-enlisted (only 3 directly from the fleet, rest were from Nuke School or priors that went to NAPs first) in the C/O 2027, according to the Class Portrait; the rest most likely goes to High School students sent to NAPs first. As to the the stats on priors with a SECNAV nom that don't receive an appointment: I'm unsure exactly but it's still possible to be turned down even if there is limited competition from the fleet. I know at least two priors that were turned down this year even with the SECNAV and CO's endorsement.
For context I applied out of High School for the C/O 2026 but failed to secure a nomination, so similar to your DS, I too was nauseated at the thought of the whole college process and simply didn't feel that NROTC was right for me so I decided to enlist to work towards re-applying for USNA. Enlisted-->USNA is not impossible by any means but defiantly has its own unique challenges. I believe most people aren't saying not to do it but simply warning you of the difficulties you may face. Will your Chain of Command support your application? What if you're underway, will you have time to work on your USNA application- especially when you're new and working on your quals? Etc. I would say "Choose your rate, choose your fate." From what I've seen CTs (intel jobs) and Nukes tend to be the majority of priors at USNA, but I could be wrong. I'd assume that's because those are more STEM type jobs and have challenging academic based "A" / "C" schools (training). Not saying there aren't other rates (jobs) that get accepted to USNA, but that CTs and Nukes tend to be the majority. If your DS decides to enlist, he should be aware that he may not be able to submit a USNA application right away, unless he goes Nuke as I believe they have many Sailors apply during their "A". I mention that because I spent over a year in "A"/"C" school and wasn't able to submit a USNA application till I reached my ultimate duty station. If USNA doesn't work out while you're enlisted, you can always submit a OCS or STA-21 package to earn a commission.
Ultimately, I believe enlisting has been instrumental to my development as a person and leader. Still waiting on word back from USNA this year, but I plan to apply again next year as enlisted if I don't receive an appointment this year. I'll avoid rambling on to much now, but feel free to PM if you have any questions or for my perspective.