I would disagree for the first part: Review usually does not happen during paid hours or is even somehow formally accredited by universities.

At my university, reviewing is explicitly mentioned to be on your own time: we cannot write any hours for it.

That honestly seems like a bigger problem, if researchers are not paid for reviewing who will do it?

My experience is that reviewers do this as part of their duties and takes place during work hours.

Universities pay you for teaching and researching. Reviewing is part of the researching.

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.