As tends to be true of much of philosophy, the core insight of Wittgenstein is not too big, I think. His argument, at least in his later work with language games, revolves around "why is it that we look for truth with such unclear language? Is it even possible to clarify our language?" And that's both Socratic and also more specific than Socrates. It's done in a very down-to-business and direct tone, which gives it that ironic sensibility, since it projects confidence in an investigation that we can easily see is going to start reducing itself to the tiniest scraps of truth by assuming so little a priori.

Within the context of his mathematical investigations this question makes a lot of sense, though: the younger Wittgenstein was studying logic under Bertrand Russell and therefore had a lot of exposure to the idea of a formalized logical totality as represented by Principa Mathematica - this was the world he lived in. And he did not seem to feel that the incompleteness theorems settled the limitations of logical formalism either.