Yeah, vanished because of their success — another example of a false cause-effect chain based in a false underlying assumptions. The odd thing is, it isn’t authored by any UK ‘researchers’.
I have had the impression that Neanderthal bands were much smaller than homo sapiens tribes. If that were the case, then although the Neanderthal were successful in that environment, interbreeding may have diluted the stock so much that it seemed to have disappeared even though successful. I just wish I had samples of my late husband’s DNA. If tested it would not surprise me if it was 10% Neanderthal. Of course, I guess I could have my two sons tested, presumably they would have about 1/2 unless I have some.