Speech has consequences. Given the good done in holding rogue "politicians" accountable, not seeing that as axiomatically desirable is at least a little bit suspicious...
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.
And not being a politician, and certainly not the one currently trying to hold the White House hostage, I don't see the public interest anyway.
If you think White House emails should be signed and archived indefinitely, that is one thing. That is not what we are talking about.