Usually when people say "corporations aren't people" I think they are confused about the need for an abstraction. But you acknowledged the need for an abstraction.
I don't imagine you are confused about the status quo of the legal terminology? AFAIK, the current facts are: the legal term "person" encompasses "natural person" (ie the common meaning of "person") and "legal person" (ie the common usage of "corporation"). In legalese, owning shares of legal persons is not slavery; owning shares of natural persons is; owning shares of "people" is ambiguous.
I don't imagine you are advocating for a change in legal terminology. It seems like it would be an outrageously painful find-and-replace in the largest codebase ever? And for what upside? It's like some non-programmer advocating to abandon the use of the word "master" in git, but literally a billion times worse.
Are you are just gesturing at a broader political agenda about reducing corporate power? Or something else I am not picking up on?