The author, when not making unsupported assumptions, cherry picks data and relies on anecdotes.
Where to start? Let's try these:
"From antiquity to modernity, scientists wrote letters and circulated monographs, and the main barriers stopping them from communicating their findings were the cost of paper, postage, or a printing press, or on rare occasions, the cost of a visit from the Catholic Church." -- Not quite: how about the fact that until quite recently, only a very small economically and socially elite class had any ability whatsoever to communicate anything other than orally, much less "publish" scientific information.
"research productivity has been
flat or declining for decades, and peer review doesn’t seem to have changed that trend." The author fails to understand the point of the article that he cites, which is that research productivity has diminished
because the ideas are becoming more difficult to find. (Consider that Einstein could do thought experiments alone in his office; finding the Higgs boson took billions of dollars and hundreds of scientists.)
"New ideas are
failing to displace older ones." First, why should new ideas displace older ones? Isn't the robustness of old ideas a sign that the latter likely are correct? That's a cause for celebration! Moreover, this point is related to the one above: in a mature science, it is really difficult to generate new ideas -- and that is precisely as it should be.
"you can’t even ask them to rate the Nobel Prize-winning physics discoveries from the 1990s and 2000s because there aren’t enough of them." It does not seem to occur to the author that Nobel prizes tend to be awarded for research that has had time (as in decades) to demonstrate its importance in a field. And how do we judge where there are "enough" Nobel prizes to rank order them?
I gave up after a few paragraphs. Peer review may indeed be imperfect, and perhaps we would be better off without it. (Or maybe not: think hydroxychloroquine and invermectin for Covid.) And rants about frustrating processes are fun to write and to read. But as a piece of reasoning, well.....