I'm still hoping for something like the "calculus of statement" described in Heinlein's "Blowups Happen." I think that a plurality of axiomatic approaches and formalisms is always better - consider the dialogue between those advocating a change to category-theoretic axioms for modern math and those that want to retain the set-theoretic ones. The debate is very productive.

So I think the world needs more thinkers-from-scratch. Shinichi Mochizuki is one such, regarding his work on the "abc conjecture." But his case makes obvious one other reason there's not more from-scratch unconventional thought: it often requires Von Neumann-level intellect to pull off.