The only talk of "public forum" comes from people who are desperate to force others to listen to them. I don't need TERFs and neo-Nazis in my feed, but they want to be there.
Occasionally, it's used by other people properly to refer to a space used by government for official purposes; I suspect much of the other use is dual purpose, that is, it intends to discredit the proper use as much as to advance a more overt purpose.
What it is good for is sending sound bites at each other.
(For emergency communications SMS is better and sufficient.)
Whether or not you believe it is unsuitable for such purposes has no bearing on the fact that government has indeed used it for such purposes, and that this imposes legal requirements on the use of those government accounts as public fora that do not apply to Twitter generally.