The Chomsky hierarchy while being but a small part of his work is undoubtedly a useful technical contribution, but I don't see it as particularly relevant for c

The Chomsky hierarchy while being but a small part of his work is undoubtedly a useful technical contribution, but I don't see it as particularly relevant for cognition and linguistics. As an example, for cognition memory constraints seem to be much more fundamental than the type of formal rules. It is also rather arbitrary: many kinds of formal languages don't fit into his hierarchy, there are many other ways to carve up the space of possible languages/grammars. I think that his general linguistic theories might share the same fate as Freud's theories: large, complex theories for which there is simply not much empirical support, making it difficult for people to continue to work on them without their originator imbuing them with his authority.