> Only a handful of special cases that have obvious "paradoxes" that cannot be explained with Maxwell's equations.
What are you talking about?
> It's not even a fully general set of equations classically, it can only handle a certain constrained motions at low velocities, short distances, and generally without accelerations.
Huh? Maxwell's Equations are relativistically invariant and cover all classical electrodynamic phenomena. The only thing they don't cover is quantum mechanics (although in quantum field theory Maxwell's Equations are still the field equations of the quantum electromagnetic field, so even there they play a role).
Maxwell's equations only apply to static states, including steadily circulating currents. It's not generally applicable without extensions to more complex scenarios such as handling time delays and arbitrary movement.
Nonsense. Maxwell's equations are the equations of classical electro dynamics.
> It's not generally applicable without extensions to more complex scenarios such as handling time delays and arbitrary movement.
The equations for the Lienard-Wiechert potentials are mathematically equivalent to Maxwell's Equations (when you put those equations in potential form instead of field form and make an appropriate choice of gauge).
Jefimenko's equations are also mathematically equivalent to Maxwell's Equations; their originator believed that the causality properties of those equations would be clearer when put in his preferred form. Whether or not he was right is a matter of considerable debate.
> The apparent "paradoxes"
Are a result of lack of understanding on the part of the people claiming and promoting them.
> are literally the reason Einstein started on his journey to develop Special Relativity
Nonsense. The problem Einstein had when he developed SR was not Maxwell's Equations; it was Newton's equations. He realized that Maxwell's Equations and Newton's equations were inconsistent. Every other physicist at the time who realized that (and there were many) believed that the way to fix that problem was to modify Maxwell's Equations and leave Newton's equations the same. Einstein, however, realized that the way to fix the problem was to modify Newton's equations and leave Maxwell's Equations the same. The result was SR, and the rest, as they say, is history.
What are you talking about?
> It's not even a fully general set of equations classically, it can only handle a certain constrained motions at low velocities, short distances, and generally without accelerations.
Huh? Maxwell's Equations are relativistically invariant and cover all classical electrodynamic phenomena. The only thing they don't cover is quantum mechanics (although in quantum field theory Maxwell's Equations are still the field equations of the quantum electromagnetic field, so even there they play a role).