Who benefits from the anonymity of the peer review process?
The readers and the editors can benefit.

I know this is a contended issue, and there are many different views.

But as you've asked specifically whether there's somebody else who is interested in the reviewer remaining anonymous, let's just look at that.

As a reader, I want the peer review to have been fair and thorough.

If the reviewer is able to review freely, without fear of comeback, then they can be much more frank. They can shoot down a bad paper, even if one of the authors or one of their colleagues could hold some kind of power over the reviewer, whether it be funding, future job applications, peer reviews with the roles switched, whatever. Anonymity may enable reviewers to be more frank, more honest, and more direct in their reviews. And that directness can be of benefit to the editors, too.

I'm not saying this is the way. I'm not saying this has to be the way. I'm discussing possibilities here.

It would be great to have some solid evidence on the pros and cons of anonymity. At the moment, there seems to be a great deal of discussion, but I don't see much science on the subject.