I'd certainly defer to you in relation to subject matter knowledge (my knowledge of number theory really only extends through 1965 or so), but this is not the sense that I've gotten from speaking with the best number theorists.

When I met Shimura, he was extremely dismissive of contemporary number theory research, to a degree that seemed absurd to me (e.g. he characterized papers in the Annals of Mathematics as "very mediocre.") I would ordinarily be hesitant to write about a private conversation publicly, but he freely and eagerly expresses his views freely to everyone who he meets. Have you read The Map of My Life? He's very harsh and cranky and perhaps even paranoid, but that doesn't undercut his track record of being an extremely fertile mathematician. I reflected on his comments and learned more over the years (after meeting with him in 2008) his position came to seem progressively more sound (to my great surprise!).

A careful reading of Langlands' Reflexions on receiving the Shaw Prize hints that he thinks that the methods that Taylor and collaborators have been using to prove theorems such as the Sato-Tate conjecture won't have lasting value, though he's very guarded in how he expresses himself. I remember coming across a more recent essay where he was more explicit and forceful, but I forget where it is (somewhere on his website, sorry, I realize that this isn't so useful). It's not clear to me that Taylor would disagree – he may explicitly be more committed to solving problems in the near term than by creating work of lasting value.

One can speculate these views are driven by arrogance, but they're not even that exotic outside of the set of people who have unambiguously done great work. For example, the author of the Galois Representations blog, who you probably know of, wrote in response to Jordan Ellenberg:

That said, there is a secondary argument which portrays mathematics as a grand collective endeavour to which we can all contribute. I think that this is a little unrealistic. In my perspective, the actual number of people who are advancing mathematics in any genuine sense is very low. This is not to say that there aren’t quite a number of people doing interesting mathematics. But it’s not so clear the extent to which the discovery of conceptual breakthroughs is contingent on others first making incremental progress. This may sound like a depressing view of mathematics, but I don’t find it so. Merely to be an observer in the progress of number theory is enough for me — I know how to prove Fermat’s Last Theorem, how exciting is that?

apparently implicitly characterizing his own work as insignificant. And there aren't very many number theorists as capable as him.