What if the gov't uses twitter as it's only diffusion platform and what if them Twitter suspends say US EPA or Education twitter handles because they violate "ToS"? Since people can't in that case comms with gov't orgs, does that encumber free speech?
If the government can't communicate because it only uses Twitter, then I think the answer is "don't do that". The government can always use its own means of communication.
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.