I think I understand what you're saying. Yes, I agree that research funded by the public should be freely available (definitely unpatentable, and maybe uncopyrightable too). I think this is a separate issue, though.

If Northwestern did the research with its own money (which does sometimes happen, I think), then it is good that Pfizer had to pay Northwestern for the research, because this funds more research. The patent is just the legal mechanism that makes Pfizer have to pay as opposed to getting the research for free.

Not necessarily. NWU is a private university, and in general plenty of private companies fund research.

In some cases, the government funding issue is relevant. Not in all cases.