Well, to be useful, wouldn't you need to be able to use it? Most people outside of physicists and physics-adjacent fields are very far away from the mathematical tools to deal with these equations.
There are whole fields to simulate one particular PDE: Computational fluid mechanics for the Navier-Stokes equation. Computational electromagnetics for Maxwell's equations. Computational chemistry for the Schrödinger equation. Mathematical finance ...probably does also other things than just simulates the Black-Scholes equation.
That's what we have computers for, numerical solutions to PDEs ;-)
NS is a case in point. No general solution, but thousands of special cases that are solved and many more that can be understood using numerical methods