So it becomes patently obvious that circuit analysts should model current flowing through a capacitor without being assaulted by curmudgeons claiming that Maxwell was wrong. Case closed.
Case misstated. Current can exist in the branch containing a capacitor without the charge actually passing through the capacitor itself. This is due to the ability of the capacitor to store and deplete charges on opposite sides of the dielectric. This action can only exist for a finite period of time in one direction, called the transient time. Circuit analysis concerns itself with branch currents, not currents present in the component themselves.
Max was not wrong about his equations, only about what he named one term of one equation. The mathematical relationship of the term is correct, however.