[Xcelerate]

1) is reducible to just the Eigenvalue problem for H. Certainly better understood than fluid dynamics.

I feel like that's akin to stating that Fermat's theorem just shows there is no n > 2 such that x^n + y^n = z^n

2) you can contrive ways of making the eigenvalue problem hard

You've got this backward. You can contrive ways of making it easy. Almost all physical problems for any system larger than but the simplest of atoms is incredibly hard.