Or a better framing: Clay Institute chose the wrong Navier-Stokes problem for a Millennium Prize.

Not really. All of the Navier-Stokes options in the Clay Institute formulation of the prize are real problems of significant interest. The history of this particular problem is of finding specific conditions under which we can get something to work that turn out not to generalize in ways that people don’t expect eg iirc (It’s been a while since I read about it) there was a solution found early-ish in the 20th century for the 2-D case that turned out not to generalize to N-d, N>2 case, there are special conditions under which the turbulent terms cancel out and you can get smooth flow, vortices etc.

It seems to me that formulating problems at the boundary of human knowledge precisely is always going to be challenging and situations are bound to occur where you look back with the benefit of hindsight and wish that you had posed the question slightly differently based on some knowledge you didn’t have at the time.

Yet it had remained unsolved until OpenAI's effort...