I imagine it was because the responses were meant to be public...
I think the recipients were happy to make their replies public. It's got to be satisfying to do it when you know that the obnoxious, melodramatic blowhard who is trying to convince his followers that he's fighting the good fight against evil bullies will grind away a few millimeters of tooth enamel watching your reply.
I think he's painted himself into a corner with this. Loudly proclaiming his intent to protect himself via legal action, he has a lawyer email a sloppy 'letter of warning' that is little more than a roll of the dice. Now he watches as the recipients mock and roast him ruthlessly in response. What does he do? Drop it and pretend it didn't happen? Make more bombastic threats? Try actual legal action? There doesn't appear to be a scenario where he doesn't find himself in a deeper hole with only a shovel in his hands.