This would be quite a feat to pull off since the private colleges are so small. Nationally, private schools make up less than 15% of all schools.
I think the power elite in the northeast come from private schools, which is why funding for public schools in the northeast is so low. In NY state, I once wrote down the names of US senators since the 60s, governors since the 60s, state house and senate leaders, majority and minority, since the 80s... and not a single one of them went to public school. Bruno, Silver, Clinton, Moynihan, McCall, Skelos, Pataki, Cuomos, D'Amato, Hillenbrand, Spitzer, etc.
This is why the state gives $50 million to Canisius and st. John's Fisher (for a new law school) while slashing tens of millions from state school and (ironically) U. Buffalo Law.
There is a real issue in the northeast. Outsiders are totally incredulous at the way things are run here. They can't believe it.
I think northeast private schools do have an impact on the lack of large land grant universities in the northeast. Many states rely on large land grant universities to be the best form of higher education within the state. States in the northeast recognize the presence of very good private schools and thus do not provide the same support to create large land grant universities. More students may still attend public schools in the northeast, but the need for a large land grant university that excels in research is not as required. The best graduating HS seniors each year in the northeast have more options and are more likely to go private, leaving the public schools with lesser students. In states that lack as many top notch private schools, the large land grant universities can recruit better students and thus bring in more research money. I also think many of the northeast states, including PA, prefer smaller schools. PSU and Pitt are not state schools, as the PA state school system is made up of many smaller schools.