> I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already.

> The perverse incentives of academia mean this has never occurred.

This. Mathematicians in their most energetic years are trying to get tenure or land a tenure-track job. They are disincentivized to go all-in on ultra high risk, high-reward problems. The potential downside is just too forbidding. It's much safer to develop a research program in a mainstream field that affords many opportunities for partial progress that can translate to a robust publication record.