For me it is incomprehensible that from the indisputable fact that a free electron - like a proton - carries a constant charge with it, one transfers this empirical finding to bound electrons (protons). In order to counter the contradiction between the repulsive charges of the protons in the atomic nucleus and the actual stability (in combination with neutrons), the strong interaction was introduced around 1970.
A stronger attractive force was postulated to explain how the atomic nucleus was bound despite the protons' mutual electromagnetic repulsion. This hypothesized force was called the strong force, which was believed to be a fundamental force that acted on the protons and neutrons that make up the nucleus. Source
How should we imagine the disappearance of charges in an annihilation process? As an entity without any transition time? Probably not. The charges as well as the solid matter of the two particles dissolve in a photon shower over an - albeit very short - period of time.
The same can also happen partially in a proton-electron process. The photons carry away not only partial mass but also partial charge, and the atom becomes what it really is when viewed from the outside - a largely neutral entity.
At what point of approach in annihilation process the charges of antiparticles disappear? How is relevant to the electron-proton interaction?
This question is in context with What are the differences between electron-positron annihilation and proton-electron scattering?