The model is basically correct. Statically charged objects either attract or repel. We have macroscopic proof of this. Then a theory was developed, which explained such macroscopic behavior, and more.Integral said:The error is not due to Maxwell, but rather your model of the atom. As usual when you make non physical assumptions you get non physical results. That is the main lesson of all your arguments.
Something about the model is right, since Bohr was able to derive the Balmer formula from his assumptions. He added a quantum physical assumption, in order to counteract the Maxwellian Catastrophe (namely unstable orbit).
We have an electron that would move in a straight line at a constant speed, or remain at rest. This is true because the electron is in an IRF, and the law of inertia is true in any IRF.
However, the electron isn't doing that, therefore it is experiencing a force.
The Coulomb law is the experimental magnitude of that force, the constant comes from experiment.
This being said, if we now further apply Maxwell's results, this electron should radiate EM waves and spiral into the nucleus. That doesn't happen.