Private School Handicap?

I’ve heard the excuse in some circles that baseball’s struggles are directly due to the fact private schools cannot put together a large roster with the 11.2 scholarship limit. It’s obviously a big burden for USC or other private universities.
But a quick check of the top 25 polls shows Rice, TCU, Gonzaga and Elon (Elon!) seem to be doing something right. And USC did make the NCAA Tournament in 15 of Mike Gillespie’s 20 seasons.