This logic does not follow. If some third-party data leak results in my social security number being published, does that mean it is now ethical for a researcher studying that data leak to post my social security number without redaction?

This is not a contrived example: Equifax was, apparently, compromised in full, which means that all American social security numbers issued prior to that compromise can safely be considered 'leaked'.

The logic follows that I should be permitted to post anyone's social security number for any reason at all, without regard for the ethics of doing so, because "it's been made public" and therefore all ethical concerns are void.

I disagree with this premise. Context of disclosure matters, even if the information has been previously disclosed. Ethical considerations apply regardless of previous disclosure.

One disclosure of personal data does not negate the ethical considerations around that same disclosing personal data, even if it has been made public at any point previously. This approach ends up supporting doxxing — where 'public' information is used unethically to target individuals for harassment.