In addition to contributing to class discussions, gifted students contribute to the reputation a school has for having smart graduates, which draws employers and therefore students. Their higher SAT/ACT scores boost the schools' USN&WR rankings.
The higher a school's ranking, the more it can charge in tuition, which partially explains why non-top-tier schools offer full and partial merit scholarships.
Agreed! With athletes, the institution fields a team, they get ticket money, all pretty quickly, possibly freshman year. With intellectuals, the larger payback may be delayed until graduation when the alumnus performs well on the job, earns positive press and accolades which also reflect on the school, and possibly becomes a benefactor. Not to say that the enhanced level of thinking and class discussions and high SAT scores of admitted freshman aren't also valuable, but they are not cash-in-hand-today like sports ticket sales.
I've seen high schools hold signing ceremonies for student athletes... not personally aware of any such fanfare or media event for intellectuals making their final decisions after considering their various acceptance letters. It may be happening, but I'm not aware of any.
To recap: I agree that high achievers should not be shut out of AP classes. Current high school ranking methods may need to be refined. I think strivers can benefit from access to AP classes if they do not slow the pace or dilute the content (possibly aided by a support class as scaffolding). I believe students need to consider whether they are contributing, and know what their contributions are (this may be an interview question someday). Unfortunately schools may have an overemphasis and focus more on athletics, as compared with sparking an interest in being life-long learners with growth mindsets.