Here's a question for you. What's your opinion on the physical reality of the magnetic vector potential?
You can ask the same question for all models. The vector potential has been introduced to get some symmetry into the math. And in fact if the problem has a high symmetry scalar effects can be modeled that way. QM also fits very good with reality if you restrict the range of the reality.
Thus: Any model that fits a problem has a certain physical reality.
My model made a prediction, the quantization of the proton magnetic moment. This is something else. Now we wait for the reality to fit the model...