Not really. And that is the problem on both sides.

Strictest competition vs Participation trophies.
Both ways have serious problems.

If all the girls go after the jocks, then those who tend toward brains rather then brawns are shit out of luck.
Why bother? Why even try?

In any one competition, there are winners and loser and those who shouldn't even bother trying.
So, in order for their to be competition, you have to have a group that is pretty much on a level playing field (weight classes in boxing) and all very interested / motivated in that arena of competition.

To place any one competition across a school, creates a class of why bothers.

---

Innovation is not born of competition. Innovation is someone seeing something and then have a stroke of insight (or a muse whispering in the ear) about an improvement on such.

Not allowing that person to take the better idea and produce it in "competition" is what stops innovation.
Competition doesn't create the innovation, but its absence blocks it.