Being a top golfer/fencer/rower/tennis player does not just serve as a signal of dedication and grit (otherwise being in the piano guild or running a 3hr marathon or being lead guitarist in a band would help just as much), but also as a proxy of parents being in the 0.1% of wealth - both because these are upper class pursuits and because they are generally expensive to train and find elite private lessons for.

And because of the culture of university endowments/donations, US elite universities massively chase the 0.1% unlike in other parts of the world.

A lot of business is done on the course and you always need a lawyer or finance person. Those who can golf get on the foursome and get the credit.

The less athletic smarter ones get sent the work.