I disagree, there's been quite a few attempts at refactoring math. Whether it's the Hilbert Program, which attempted to formalize the foundation of mathematics,

I disagree, there's been quite a few attempts at refactoring math. Whether it's the Hilbert Program, which attempted to formalize the foundation of mathematics, the Cartesian plane as a way to describe functions in space or the modern reformulation under homotopy type theory, mathematics has gone through some serious refactoring. Even something as simple as algebra has gone through extreme changes in notation and in phrasing. Try comparing a copy of Euclid's elements to your standard geometry textbook. Or a proof of the Galois Correspondence Theorem in an Algebra textbook to the original in French. Also, I highly doubt that math would significantly simpler or "logical" (a rather peculiar word to use, as math is inherently about logic, so what would more logical logic look like?). Math is inherently about communication and is therefore inherently subjective. People have a million different ways of writing math because they have a million different ways of speaking. And depending on who you ask, one way may be more simple or more logical than another.