The claim that “classical physics says magnetic fields shouldn’t do work” is false. What classical physics says is just that a magnetic field does no work on an isolated single-point charged particle (because a charge at a single point has no magnetic moment and the magnetic force on such a particle is always perpendicular to its direction of motion). But this does not preclude the doing of work on a wire loop carrying a current or on a rotating charge distribution. [To create such things though requires us to have some mechanism for confining or holding together the relevant charges, and although classical physics did not say these things were impossible it never got to the point of including a description of the required additional non-electromagnetic forces. Quantum mechanics, on the other hand, did provide a means (without even requiring non-electromagnetic forces) for describing situations in which charges could be confined in atoms or metallic solids (and even predicted that an isolated point charge would nonetheless have a nonzero magnetic moment).]