Are there any public universities that require this?

I went to a public university that required students to live on campus until their junior year.

Where?

Louisiana.

http://www.uno.edu/housing/residency-requirement.aspx

Other schools in system have a similar policy.

Ohio State requires it for two years and it's about as big and public as you can get.

UMass Amherst required it of freshmen and sophomores when I was there in 2007-2011.

Weird. What practical purpose does this serve?

Do we know what lead to this policy becoming commonplace?

As an on-campus student I didn't know any off-campus students except one who went to my high school, and he didn't have many new friends from university that he kept in touch with. It is difficult to overestimate the social aspect of universities, which has led in part to other changes such as a common core curriculum for all undergraduates, for instance.

I'm not claiming that students should live on campus, but there are clear advantages if they do so to both those students and other on-campus students.

In theory, the argument is that it creates initialisation conditions of greater social and academic engagement that increases the likelihood of staying in college and completing a degree. The idea is that clueless freshmen who have never lived independently before and are unleashed for the first time will just get lost to the party if you set them loose off campus. This way they are given some structure and discipline during their first year or two in college, ideally creating a healthier template they more likely to adhere to in some measure even after they move off-campus.

Practically, it's more likely just a revenue measure...