Also, calling "generative grammar" productive seems wrong to me. It's been around for half a century -- what tools has it produced? At some point theory needs to come into contact with empirical reality. As far as I know, generative grammar has just never gotten to this point.
Generally, I absolutely agree that he is not humble in the sense of expressing doubt about his strongly held beliefs. He’s been saying pretty much the same things for decades, and does not give much room for disagreement (and ofc this is all ratcheted up in intensity in his political stances). I’m using humble in a slightly different way, tho: he insists on qualifying basically all of his statements about archaeological anthropology with “we don’t have proof yet” and “this seems likely”, because of his fundamental belief that we’re in a “pre-Galilean” (read: shitty) era of cognitive science.
In other words: he’s absolutely arrogant about his core structural findings and the utility of his program, but he’s humble about the final application of those findings to humanity.
Contrast to the statistical approach. It's easy to point to something like Google translate. If Chomsky's approach gave us a tool like that, I'd have no complaint. But my sense is that it just hasn't panned out.