Magnetohydrodynamics is, specifically, the "easy part" carved out of plasma fluid dynamics. It is inadequate to almost all applications, with only rare, precious exceptions, mostly manufactured. Devices that rely on plasma fluid dynamics to work are carefully designed to keep the plasma in the domain where MHD can be used to model them.
Astrophysicists, as a rule, hate to be obliged to consider phenomena that involve plasma fluid dynamics, even what can be shoehorned into MHD. Such phenomena are thus orphaned, and you won't find anybody talking about them.
The exception is solar physics, where nothing can be done at all without fully general plasma fluid dynamics. Solar physicists have the largest gonads in science, on par with rocket propellant chemists.
I think most consider it "somebody else's problem". I know some don't like to think there is anything to it beyond MHD, so they call anything involving plasma "MHD".
Are there other phenomena they see but don't like to talk about? Maybe?
It has several commonly unphysical assumptions, including infinite conductance, "freezing" the magnetic field in a chosen frame, and assumptions about time and length scales.
"Effects which are essentially kinetic and not captured by fluid models include double layers, Landau damping, a wide range of instabilities, chemical separation in space plasmas and electron runaway."
That electrons are 1836 times less massive than the lightest positive charge carrier is neglected. Accelerated, they strike positive and neutral particles and knock loose more electrons.
Astrophysicists, as a rule, hate to be obliged to consider phenomena that involve plasma fluid dynamics, even what can be shoehorned into MHD. Such phenomena are thus orphaned, and you won't find anybody talking about them.
The exception is solar physics, where nothing can be done at all without fully general plasma fluid dynamics. Solar physicists have the largest gonads in science, on par with rocket propellant chemists.