Charge is (basically) conserved, so if you start with a non-charged star you need a non-charged result. All ordinary matter is close to balanced in charge. (Even things on earth with a really high voltage)

As for why not a mix of both, neutrons are just more compact. Literally, as the start collapses, the massive pressure “squishes” protons and electrons together, and they undergo the reverse of a radioactive decay. It’s just because that’s more energetically favourable than taking up the extra space, and a neutron results.