Everett achieved something unequivocally difficult--after twenty years of failed attempts by other missionaries, he was the first Westerner to learn Pirahã, living among the people and conversing with them in their language. In my view, that gives him significantly greater credibility than academics with no practical exposure to the language (and I assume you're aware of his response to the paper you linked).
I understand that to Chomsky's followers, Everett's achievement is meaningless, in the same way that LLMs saturating almost every prior benchmark in NLP is meaningless. But what achievements outside the "self-referential parlor game" are meaningful then? You must need something to ground yourself in outside reality, right?
> Then when we finally get to see the concrete alternative proposal, it turns out to be nothing more than a promissory note.
I'm certainly not claiming that statistical modeling has already achieved any significant insight into how physical structures in the brain map to an ability to generate language, and I don't think anyone else is either. We're just speculating that it might in future.
That seems a lot less grandiose to me than anything Chomsky has promised. In the present, that statistical modeling has delivered some pretty significant, strictly falsifiable, different but related achievements. Again, what does Chomsky's side have?
> I don't see how we can discuss this question without getting into specifics, so let me try to push things in that direction. Here is a famous syntax paper by Chomsky: https://babel.ucsc.edu/~hank/On_WH-Movement.pdf
And when I asked that before, you linked a sixty-page paper, with no further indication ("various things"?) of what you want to talk about. If you're trying to argue that Chomsky's theories are anything but a tarpit for a certain kind of intellectual curiosity, then I don't think that's helping.