> Just insist on Lean (or some other formal verifier) proofs for everything.
This is not an easy change at all. Some subfields of math rely on a huge amount of prereqs, that all have to be formalized before current research in that field can insist on formal proofs for everything as a matter of course. This is the problem that the Lean mathlib folks are trying to address, and it's a whole lot of work. The OP discusses a fraction of that work - namely, formalizing every prereq for modern proofs of FLT - that is expected to take several years on its own.
This is not an easy change at all. Some subfields of math rely on a huge amount of prereqs, that all have to be formalized before current research in that field can insist on formal proofs for everything as a matter of course. This is the problem that the Lean mathlib folks are trying to address, and it's a whole lot of work. The OP discusses a fraction of that work - namely, formalizing every prereq for modern proofs of FLT - that is expected to take several years on its own.