There are definitely many low income kids who thrive at Grid iron football. Lots of poor Latin American kids play baseball.
The sports that require alot of money to play are mainly ways for upper class white kids to avoid having to compete against the black kids and still feel like they are good athletes. At least in the US.
Not to mention rowing, cycling, biathlon, triathlon, sailing, equestrian, mountaineering, etc. I don't know the exact numbers offhand, but it seems like the vast majority of elite athletes come from wealthy families and go through colleges like Yale and Stanford. The only sports that have even nominal representation from low-SES backgrounds are made-for-TV sports, but if you look at the overall picture it's not nearly as egalitarian.
In sports like golf, gymnastics, figure skating, hockey, gridiron football, tennis, skiing and snowboarding it's another story.