If an atom has a +1 net charge, meaning it is missing an electron, why doesn't it just drop a proton?

Electrons are moving around the nucleus, and thus electrons can be lost from an atom readily in chemical reactions.

In nucleus, the binding forces between the nucleans (protons and neutrons) are strong, and thus protons cannot be dropped from an atom in chemical reactions.

Why would it do that? There is a great deal of energy holding that proton in.

Atoms are not sentient, and they don't care about their charge. What force would cause them to "drop" a proton?

then it wouldn't be an atom of whatever element it is.