I don't think a replacement is needed. If your communication is important to a lot of people, it shouldn't be just immediately jammed into 280 characters using your thumbs while sitting on the toilet or whatever.
Post it on congress.gov using some inefficient boring process or whatever the official communication method of your role is.
Pass regulation that puts in a place a federated messaging infrastructure, so that Twitter users can subscribe to messaging from Government official that sends out messages via an external system.
I don't disagree, but with what?
It's easy to say this is 'wrong/broken', but I don't see a great fix other than people 'rolling their own solution' and that's not realistic.