Why does atomic charge not balance in nuclear reactions?
There are two reasons why nuclear reactions don't consider (or often account for) charge.

The first is that charge is usually irrelevant to the reactions. If we are looking at changes in nuclei we can for all practical purposes ignore the electrons that would be associated with the nuclei under normal conditions. They are just irrelevant to the nuclear reaction taking place.

The second is that they do account for charge, but only in nuclear processes. Some radioactivity (isolated neutrons decay or any nucleus undergoing beta emission) can lead to the decay of neutrons into a proton and electron and some other minor particles. The electron clouds that would normally surround the nucleus are still irrelevant to these processes but the equation for the nuclear reaction should account for the emitted particles. When writing these equations only the nuclei (and the emitted particles) are accounted for and any net change of charge is ignored as a description of the nuclei involved implicitly describes the net nuclear charge (in the same way that many organic chemical structures don't explicitly draw every hydrogen as chemists can fill them in knowing that the total valence around carbon should add to 4).