You seem to be making the claim that LLMs are statistical text generators, but statistical text generation is good enough to succeed in certain cases. Those are different arguments. What do you actually believe? Are we even in disagreement?
So you agree that LLMs are in fact statistical text generators but you don’t like people use that fact in arguments about the capabilities of the things?
But it is no longer useful to bring that fact up when conversing about their capabilities. Saying "well it's a statistical text generator so ..." is approximately as useful as saying "well it's made of atoms so ...". There are probably some very niche circumstances under which statements of each of those forms is useful but by and large they are not and you can safely ignore anyone who utters them.