When you want to reach people you go to where the people are. You fish where the fish is. It is that simple. People did not join twitter because the police was posting there, the police post on twitter because that is where they can reach the people.
That I can agree with. Usually what I have seen, at least where i live, is that no public body used it exclusively. They still had a website, they still talked with journalist, talked with radios, used flyers, whatever was appropriate in each situation. (Or at least they tried, not saying everyone was getting it always right.)
I've been annoyed over the years because (not having an account) sometimes Twitter won't let me look at Tweets. Hopefully none of them contained useful info.
These public entities post _exclusively_ on Twitter as if it's the public square. It's not and it shouldn't be. The argument is not about how easy it is to create a Twitter account.