I don't understand the reference to Gödel. Do you mean the theorem that in every formal system capable of representing arithmetic there exist sentences "P" such that neither "P" nor "not P" are derivable in the system?

It doesn't seem to me that from this it follows that "the point of philosophy is better living". It might be obvious, but I just don't see it.

I like to think of it as all formalisms are tautologies. Therefore we can go along with some common sense and fuzzy logic rather than having to prove every possible axiom, which isn't actually possible or would take unlimited time. It's analogous to the halting problem.