No. Peer reviewers get: early access to articles of interest, the feeling of contributing to the community they belong to, the ability to demonstrate their knowledge, the ability to reciprocate other people for reviewing their own articles, and so on. These are not financial rewards, but they are not less strong for that (arguably even stronger).

Journals are heavily incentivized to maintain standards because otherwise good authors will stop submitting to them and librarians will stop subscribing (of course only the first incentive holds for OA journals).

The fact that system sometimes fails is not proof that it is a bad system - all human systems have a failure rate.