There's a different angle to this that you aren't seeing.
Many of the student-athletes that attend service academies have different reasons for doing so than the non-athletes.
I've already outlined several of those reasons and examples in prior posts.
Furthermore, as I've already pointed out, standout athletes that are recruited to the academies are afforded considerations in the nomination and admission process. There are relaxed admission standards in place in an effort to become more competitive in sports. A quick google search revealed the following article from 2013 detailing a bit of what I'm talking about:
https://www.nytimes.com/2013/12/19/sports/ncaafootball/for-army-football-a-duty-to-win-again.html
You don't seem aware of any of that. You also don't seem to have first hand knowledge and accounts, as I do, of student-athletes that are making these choices and the motives and reasons behind those choices. My advice is to you do some research.
My son graduated HS in 2013. One of his good friends graduated a year later in 2014. His friend was arguably one the top 2 or 3 players on the team and he received moderate recruiting interest. But he didn't end up landing a formal scholarship offer from a couple of the schools he really wanted to attend. Only a PWO from one of the schools w/o a reasonable promise of future scholarship. His family didn't have the means to pay out of pocket and financial assistance wasn't sufficient. Meanwhile Navy had been recruiting him very hard beginning his Junior season.
He ended up choosing Navy. But it wasn't his first choice. And he didn't work for years to get that opportunity. That's the point you guy keep missing with regarding to athletes and recruiting.
While this kid did end up playing ball for 4 years and graduated a couple years back, there are many others that don't stick it out and realize they made a mistake. I personally know of dozens of examples and only mentioned a couple.
But they largely received the opportunity because of their athletic prowess (academies have been taking greater chances on prospects than in the past) and some of the kids only took the opportunity in order to play D1 FBS football.
Believe it or not, some kids buy into the idea that it's more prestigious and impressive to play ball at an FBS program rather than FCS or D2 or D3. So when their options at FBS are limited, some end up choosing an academy for the wrong reasons. And because the academy is trying to win like everyone else, they take a chance on them. Sometimes it works out, sometimes it doesn't.
FWIW, here's a informative article from 2017 detailing how recruiting at service academies works:
https://navy.rivals.com/news/understanding-service-academy-recruiting
When you read that article and notice the rise in commitments, it's not hard to connect dots and realize that not all those kids fit into the box you believe they do. Many of them weren't longing to go to a service academy for years. And they didn't put in tireless work to get the opportunity.
So your blanket statement of "This isnt why people go to the academies" is not universally true. It might be true of whomever you know, and it might be true for some student-athletes, but it's far from true for all.
That was my point from the very beginning. Period, end of story.