Many/most laws in the US are selectively enforced. A university police force is a prudent way for many/most universities to have university matters taken care of in a way that suits the university. Typically this means doing a lot of menial things (e.g., dealing with underage drinking, esp. in public) that might create liability or a PR nightmare for the university that the local police might not be inclined to deal with. The university police can often be more likely to de-escalate certain matters than local police, and this is generally a good outcome for the school.

At wealthier universities, this is also a way to convince parents that their kids are safe. Harvard, Yale, Penn, and Stanford (off the top of my head) are all in or near not-so-safe neighborhoods -- although gentrification of those areas are making this less of an issue these days.