Is there anything about the implications of the "early" quantum theory of Schrodinger equation, wave-particle duality, or the two slit experiment that conflicts with the idea of a point charge? Did the realization that electrons and protons have size emerge from a conflict of principle between classical E&M and foundational ideas of quantum theory? Or did the realization of size of subatomic particles emerge from developing the best model from later experiments, perhaps with accelerators, nuclear reactions, ...?
I'm sure that there is a more precise way to describe the issue I'm asking about but I only have a very superficial understanding/awareness of quantum theory and modern physics. My question is motivated from my studying E&M from Purcell and Griffiths.