@LucieTheLakie, most of the SUNY’s are young. Most didn’t become major full-fledged research universities until after WWII, and I can’t think of any school that was established after WWII that is a powerhouse in any major collegiate sport. This is true on the other coast as well. UCSD is a more impressive research university than most state flagships, but they’re not a powerhouse in any sport.
As for whether playing big-time sports will attract more OOS students, we have a natural experiment in Rutgers.
Certainly, football did a lot to propel PSU from being an ag college located in the middle of nowhere to being a major research U that is attractive to many OOS students.