An even better analogy would be a mailing list, instead of directly emailing/cc-ing recipients. Definitively not "private messaging".
If I delete my email account, and/or remove it from the list, there's no expectation that my prior emails are deleted for any of the other list subscribers.
The mailing list archive isn't pruned of my account and everything I ever sent will still be visible.
You’d have the right to request removal of your messages from the central mailing list archive (I believe), but not the copies received by the individual mailing list subscribers.
With Discord, all messages are in the “central archive”, there are no individual copies.
If I delete my email account, and/or remove it from the list, there's no expectation that my prior emails are deleted for any of the other list subscribers.
The mailing list archive isn't pruned of my account and everything I ever sent will still be visible.