While some of @PurpleTitan 's observations are valid, I think he or she has some things fundamentally wrong, too. Harvard in 1636 was democratizing because students who were neither Anglican nor Catholic were effectively barred from university education in England. It represented an effort to construct a Puritan leadership class based on education and scholarship, not inherited wealth and title. The great American universities of the 18th Century played a critical role in nurturing a class of American leaders who did some pretty cool things.
But the design and concept of the modern university really dates from the educational reforms of the 19th Century, reforms that were embodied by Cornell and that led to the founding of Stanford, Chicago, Vanderbilt, MIT, and many state universities. They were democratizing in opening up membership in the social/political elites to people of talent who weren’t Lowells or Cabots. It wasn’t broad-based, not yet, but it was broader and more vibrant than strict class hierarchy would have permitted. And all of Karabell’s stuff about how Harvard started doing holistic admissions to restrict the number of Jews there reminds you that Harvard was actually admitting quite a lot of Jews 100 years ago (including my grandmother, all three of her brothers, and a future brother-in-law), when Jews were still openly excluded from many fields of commerce and government. Yes, they were well-to-do, but they were not part of any hereditary elite – my great-grandfather whose children went to Harvard had maybe the equivalent of an 8th-grade education in rural Lithuania.