Public officials should be completely banned from using communication systems that are not state owned for professional purposes. It makes absolutely no sense that politicians use Twitter as an official communication channel.
Especially when during campaigning it is necessary to grow that kind of following organically and to leverage social media. Saying that the day you get elected that you must disable your online presence feels like the wrong solution.
I do think there should be some higher standard though. I just am not sure what it is. The same threats exist in Email that exist on Twitter in a lot of ways. I can register "JoeBidden.com" and email you about "my" campaign all day. There's no official registration of your "official" domain anywhere. And even if there were, that can be hacked too.
You are trying to close Pandora's Box.
This was exactly my first thought when I saw Sen. Hawley's open letter to Twitter, aghast at the idea that the President's own account could be affected by this. I share his concern, but not his determination of blame. It is not a private company's job to protect the communications of our government. It is the job of our government's defense and intelligence apparatus. They can't do that job without the requirement for communication to be done through channels they control.
Anything is possible through legislation, I'm not sure this is such a big leap.