Personally I don’t see the quid pro quo nature of peer review (you review in return for your stuff being reviewed) as a problem. But I dislike the fact that the publishers limit access to something that others provided without compensation. Seriously their subscription models are outrageous, nothing they provide alongside the actual content makes it worth it.
Not all reviewers even work for universities. Some of us are in industry, and our companies certainly don't pay us to anonymously review scientific papers.