Check any quantum optics book. There are real experimental effects that cannot be explained by not quantizing the EM vector field along with the electron spinor field.
One example is entangled light like in the Aspect experiment.
You cannot explain nonlocal photon pair polarization and also momentum correlations with classical EM stochastic fields.
e.g. one of the Bell states
|12> = (1/2)^1/2(|1+>|2+> + |1->|2->]
with +- a linear polarization basis defined by orientations in space of linear polarizer.
