I think it is time to return to the pre-Twitter days.
That's what most people appear to use it for. Stop using twitter and join a social network or news source or whatever you want that meets your needs. Or form a closed twitter group that doesn't include politicians.
I think twitter in particular has destroyed modern discourse, but we're not going to ban our way out of this.
It's true that politicians and their followers have dumbed down discourse (and to a stunning degree) but ultimately it's the consumer of that discourse who needs to change and Twitter is not standing in the way of that.
I don't "tweet" or follow Twitter much at all but I think it's fair to say that on any given day there is a lot of very useful, helpful, and positive banter going on there.