S does admit student athletes from

top public schools. I know for a fact that almost every year S SCEA at least one student athlete from a top public school. But you must be a top athlete in a particualr sports. It may not be a team sports. For example: 

rowing 

golf

gymnastics

track

swimming

S does the same thing with award-winning artists, poets, dancers, authors, ....

The truth is that S wants to compete against H in humanity disciplines.

S just does not give STEM students any special treatment since S attracts so many of them.

A student athlete major in STEM is a rarity but a pool of hundreds of smart students from a top public school makes it a certainty.