That said, I had an instructor who started the first course in electricity in magnetism by writing out the Maxwell equations, then working through them down to the Coulomb's law and other special cases, which is the opposite of the standard approach. But he knew what he was doing and was careful to only inflict the minimum necessary amount of math and rigor on the poor unsuspecting suckers in his class. I do not know of anyone deriving F=ma from the least action principle at an introductory physics course, though it seems doable.