I read the paper, the references, even extend the search for references, and provide my constructive feedback through the eye of my own experience. That could not be done by AI by any stretch of imagination.
Yes. AI has no experience so it cannot apply it through its own eye. On the other hand, AI can do many useful things. It can point out some of the problems you might find. It uses an entirely different set of procedures, because it is an alien form of intelligence (if we grant it is any kind of intelligence).
The Microsoft Word Review, Spelling and Grammar check feature can also do many useful things. It is far less capable than AI, yet some of the corrections and suggestions it makes are similar to what a good copy editor does, and some are even what a peer-reviewer does. It reduces the need for peer review. It partially automates some aspects of peer review. I think it is an overstatement to say that AI and Microsoft Word Review cannot do any degree of peer review, "by any stretch of the imagination."
AI and Microsoft Word are inhumanly thorough. If they are capable of finding a problem at all, they seldom overlook it or forget to mention it. I have seen AI forget to translate part of a Japanese document into English. It left out a clause. When I pointed this out, it put the clause in and apologized.
I expect AI will make rapid progress. In a few years it will be able to do most kinds of peer-review as well as a human. It will have a synthetic form of experience. Perhaps I should say "simulated experience." If this simulated experience is functionally similar to your actual experience as a human being, and based on the simulated experience, it reaches useful conclusions similar to what a person would reach, I do not see why it would matter that the experience is simulated. Functional equivalence is fine with me.