I think all public schools should have pay banding based on cost of living with some exceptions. None of this stuff is mutually exclusive, as "education quality" is based on reputation and other factors, and funding is based on research findings that are being sponsored by the private sector and so on. There are going to be exceptions, like business schools that are entirely self funded and thus have to pay competitive rates vs other programs.

In a perfect world I would be of the opinion than the government provides guidance to the schools that are supported by public funds but leaves final decisions to them, the students, and the communities they support. In a world like that I'm sure you'd see tenure mean a lot less and allow for adjuncts (who teach the majority of classes) to receive a living wage which they currently dont.

Obviously Harvard doesn't apply to this discussion as private institutions are exempt from the "tax-payer funded" argument. Private schools can do whatever they want as they're private entities, if they want to compete in sports against the public schools they have to abide by the public school rules.