Certainly they could revert to phone and snail mail, which was the prev status quo. However, that would be to the detriment of the people.
But I don't think we'd consider that a solution.
Except for the part where no one would pay attention to it because it's Twitter, and the part where the government controls the platform, making internal surveillance and censorship inevitable. It would probably just wind up a PR machine for the party in power.
But government employees, from the President all the way down to, say, interns having an official and direct means of communication with the people, on public record? I'm all for it.