I am not arguing that people should be paid public money to do Chomskyan linguistics. That is an entirely separate question from the question of whether or not Chomsky's key claims are true and whether his research program has made progress. Again, you will have to throw out the majority of science if you hold to the criterion that only work with practical applications has any value.

I also think that you continue to underestimate Chomsky's overall influence on cognitive science. If you think that post-cognitive-revolution cognitive science has achieved anything of note, then you ought to give Chomsky partial credit for that.

>I don't see how that small number of examples is supposed to scale to an entire natural language

Wide coverage generative grammars certainly exist, though they were never something that Chomsky himself was interested in. Here is one in a Chomskyan idiom: https://aclanthology.org/P19-1238.pdf

I'm still puzzled by your point about falsifiability. I haven't seen anything close to a falsifiable claim from people who are excited about the cognitive implications of LLMs. The argument is little more than "look at the cool stuff these things can do – surely brains must work a bit like this too!" Read almost anything by Chomsky and you'll find it's full of quite specific claims that can be empirically tested. I guess people get excited about the fact that the architecture of LLMs is superficially brain-like, but it's doubtful that this gets us any closer to an understanding of the relevant computations at the neural level.