It's very expensive to start a college. Most superrich can get their kids in or influence research or whatever they want to do more efficiently by donating to existing schools.

Another alternative is to fund a lab or think tank with no students.

I'd argue most newish schools are set up because their founders wanted to promote a new kind of education (Olin College's hands on engineering program, Liberty University's Christian environment, etc.) not just start Yet Another Prestigious University