Most vendors license based on students served, not public that pays taxes. If a university is licensing content based on the number of students or faculty at the university, it's likely that they are not allowed to offer it to tax payers. I understand your point is that you are paying, but that will not mean you can walk into a university and demand access. They would need to renegotiate with the vendor.

Many public universities allow public access to all resources when you are physically at the library. Their licenses are broad enough (and expensive enough) to allow access to anyone from campus. Also, if you're on campus, it can be difficult to determine who is a student / staff, etc...