1) These universities tend to be land-grant institutions that were created in rural, not urban areas, although the surrounding "college town" may have subsequently become urban or suburban.
2) Public institutions due not usually have the same ability to buy adjacent land as private institutions. Many private institutions purchase adjacent real estate as part of endowment investment or to prevent undesirable neighbors.
3) Land-grant public institutions were designed to make higher education more accessible to non elite (in most cases, white) students. My argument is that the neighborhoods around segregated southern private schools developed into desirable neighborhoods for high-income residents or in the other cases, these institutions were deliberately placed near the wealthy neighborhoods they drew from.
1. Demographic and economic information about areas near major private universities.
Story on Rice Management Co.'s development of Rice Village as high-end retail: https://www.bizjournals.com/houston/news/2017/07/07/retailers-strive-to-be-near-houstons-most-affluent.html