I'll concede you're right with some caveats. Miami hasn't competed in a while, at least since they stopped cheating with impunity, despite being in one of the most fertile recruiting cities in the country. ND is the epicenter of football, and although they are technically a private school, their reach I would argue is greater than every other major program. ND can walk into any state and pull a player, not something the Cuse, Dukes, NW, etc. can do. USC also benefits from being in a recruiting hotbed, and plays the Hollywood card. I realize this is a stupid argument for them, but they feel like a big state school, more so than a private. Great branding has done them well, not to mention 11 national titles. USC and ND are certainly the outliers of the private schools.