I think it's not that obvious. For example, Maxwell's equations represent essentially a complete description of classical electrodynamics. Even though in most f

I think it's not that obvious. For example, Maxwell's equations represent essentially a complete description of classical electrodynamics. Even though in most formulations it involves densities, it will work fine for point-like charges where the density is singular but integrable. Of course, when QM comes in the theory expands to quantum electrodynamics (QED), but Maxwell's equations match very well (exactly for linear media?) the quantum mechanical predictions when you average the probabilities. It sounds reasonable to expect a fluid theory that explains well macroscopic phenomena, even if the fluid really is granular, where we could hope the approximation would hold on average or something like that. But apparently it turns out that N-S doesn't model important qualitatively distinct phenomena.