Private emails are not speech. Are you suggesting all private conversations should be public? That seems absurd to me. Do you subscribe to the "surveillance isn't bad if you have nothing to hide" concept?
All private conversations shouldn't be published. That isn't necessary to hold people accountable for dangerous or violent speech.
Publication and repudiation aren't the same thing.
Yes, it might make it harder to punish death threats, but privacy is too important to sacrifice.