Is a beef-only diet a good idea for the general population? Probably not. Could it be ideal for people with extremely rare auto-immune conditions that have an allergic reaction to virtually everything else? Sure, and that existing doesn't sound crazy to me at all.
I've noticed a trend where scientifically minded people tend to get hung up the "proven" at the expense of the "plausible", forgetting that everything they rightfully treat as proven once could have been dismissed in a similar manner. Real people in the real world have to make decisions based on nothing more than plausibility all the time, and I don't see why diet should be any different. Particularity if none of the "proven" solutions are working for you.
Put another way, there's a difference between "the evidence says this is wrong" and "there is no evidence that this is true".
I don’t think Peterson is promoting the carnivore diet, but I did hear him explain his diet on a podcast and it seemed pretty couched in curiosity, not resolution. The thing I remember is lots of “I don’t knows” and attribution of any benefits to it being an elimination diet vs any special property of beef.
He also says its not a healthy diet in general and that he doesnt know if it will work for other people.
I think a lot of people try to twist his words(or assume the worst interpretation) even on "normal" topics because they dont like his Politics.
So why beef only wouldn't work?
I have autoimmune diseases myself and have a very meat heavy diet, to me is what works, as soon I move to a more typical diet my health declines quickly.