Then you can pull the money from Berkeley, I guess. Other than that, the large majority of the very-top-tier schools are private. Yes, they receive public money for research, but the undergraduate "experience" is funded by tuition, endowment, and donations.
Still, I agree. This seems like a fantastically inefficient way to meet people with different backgrounds.
Roughly half the public money for "research" is actually pocketed by the university and spent on education/administration/etc (the university calls it "overhead"). This is a dirty little secret of science funding - a big chunk of it isn't funding science at all, but is merely a subsidy for big research colleges.
Also, even tuitions at private colleges are massively subsidized - the subsidies just follow the students (e.g., subsidized student loans, need-based aid, etc).
Still, I agree. This seems like a fantastically inefficient way to meet people with different backgrounds.