The German universities do have such a thing: They fund a network with their own backbone and all, called DFN. This organization does have a full CA root certificate which is signed by the globally trusted Deutsche Telekom CA. The DFN then signs certificates for their members. So in short the German universities operate their own CA. I don't think running this is prohibitively expensive as almost every university is member there.

Page in German: https://www.pki.dfn.de/ueberblick-dfn-pki/