[neutronicus]

You also need to include how charged matter affects the forcing fields in Maxwell's equations (i.e. moving charges depositing a current field).

I actually basically agree with your viewpoint, I studied Plasma Physics in graduate school in a regime where we did _not_ use Navier-Stokes or constitutive relations and everything was in fact just little smeared-out packets of charge moving according to the Lorentz Force Law and radiating.