A few years ago they did, but Google, Microsoft, and some of the cloud LMS companies have started to shift them onto the cloud.
As someone who had a university IT dept as a client, it's honestly much better for the school. University IT is almost universally a disaster and bottleneck.
It’s a mix. Current ERP solutions for higher ed are offered self-hosted or SaaS. Ancillary solutions are moving quickly towards SaaS only. Larger R1 schools are more likely to have solutions they built entirely in-house. Most schools have highly customized versions of COTS products.
Source: I work for a leading supplier of those solutions.
As someone who had a university IT dept as a client, it's honestly much better for the school. University IT is almost universally a disaster and bottleneck.