That is not a good way. It is an oversimplification that is vulnerable to a nuanced definition of naturalization. That definition does not allow for the rebutal of the "if a person is a citizen at birth they are not naturalized" argument.
The above simplification does not reflect the realization that the person is a citizen at birth because of naturalization laws that declare him/her so. That is why there is a special term for the group of citizens with a natural allegiance at birth, those born in the US to citizen parents. They are American citizens wholly and can be claimed by no other nation.
so, if a couple goes to France on a vacation and the wife bears a child there, the child’s US citizenship.status.be ones clouded? I don’t think so.
I’m not over-simplifying. I’m simplifying. The reason is to get to the core issue. The core issue is that you are either a citizen by virtue of the conditions of your birth, you are a citizen due to a naturalization process, or you are not a citizen.
The question is, which of these three is Cruz?
those born in the US of citizen parents...
and that is it. No operation of law is needed to define their citizenship.