I think a lot of people don't understand, with respect to a mathematical theory, the relation between a carefully stated conjecture requiring formal proof vs. using the objects in the theory effectively. Could better understanding of NS lead to better practical tools? Almost certainly, even if only to give us bounds on performance. Has its unresolved status stopped us from using NS? No. Almost no one using it cares. Resolving it is valuable, especially if it comes with mathematical and/or physical insight leading to greater understanding. But it is not this is grand result that like instantly unlocks 100+ day weather forecasts.
It would be like saying proving ergodicity more generally for physical systems would unlock condensed matter physics, ignoring how well stat mech has served us regardless.
I am not anti-AI and I don't think we should stop throwing them at conjectures. I'm against this fundamentally misleading type framing that's become prominent. Millennium prize problems are important. Treating this specific aspect of NS as the one missing piece is just harmful. If we just throw compute at formal conjectures voila cancer and fusion.
I think the better example of "AI" usefulness toward solving problems is AlphaFold, and immensely powerful tool. But also suffering from a false framing/marketing problem as "solving protein folding". It feels like the right use of compute. Considering many factors that we can't hold in our head at once. "Solving" something that was already "solved" via computation (simulation) but now much more efficiently. The output is a valuable tool itself, it was not about "solving the protein folding problem", which it didn't do. It is a tool to solve problems requiring a sequence->ground state calculation. Which is a very broad set.
Formal verification of a conjecture we set up as a benchmark we set to test human understanding is not valuable in the same way.
I'm failing to make multiple points and gotta run, but i think that final point is important. The millennium prizes are not about technological/practical value, at least not intentionally. They're about shit that seems fundamental to us, things that feel[1] to us based on our understanding are important AND feel like they should be solvable in a human-comprehensible way. So formally resolving them with pure compute is not really the point. It seems closer to that story about one of those prime conjectures where some guy just ran brute force enumerations to find a counterexample. Valuable for sure, time-saving. And knowing the answer makes it a lot easier to solve a problem.
TL:DR science and math are more than formally resolving conjectures, they're about building up understanding and tooling that you can then build more on. AI should be an increasingly big part of it, but declaring "AI will solve fusion because it's smart" is like the rest of the fucking owl meme. I have no doubt it will help, most likely via simulations/quicker testing/calculations and verification. Maybe partly via reactor designs. Maybe partly being fed conjectures about bounds/limits that would be useful as inputs for the next iteration. And maybe even in the form of resolving some formally stated conjectures (I don't know enough plasma physics to name any).
[1] obviously to the mathematicians it's more than a feeling..