Earlier quoted context omitted.
Machine checked proofs only work for deductive, non-experimental disciplines. You can't use machine checked proofs to tell if a drug is effective or not. Human referees have to be involved no matter how advanced the AI is.
You can precisely "quarantine" the "human referree part within the framework of a formal proof. That's still a huge step forward from the status quo of reasoning and opinion being smeared together and nothing formal.
I think it is unlikely you can separate the two precisely. If it be so, mathematicians can replace doctors who make diagnoses. I don't think all empirical facts can fit nicely into a formal proof system.
But still, any effort to reduce the burden on the human referees would be welcome. This said proof system for peer review would be most useful to math and theoretical CS (though not so much to biomedical sciences).