I don't really think that a state should run a service about what's happening right now but I think that Twitter is invaluable service to the public that needs to be dealt with carefully.
Twitter's power is well beyond the power of displaying ads to users and the only failing thing is the business of displaying ads to users in exchange for money. Twitter's core function is strong, it's not a failing product.
Twitter has been a prime source of first-hand real-time information in many many crises. Just because you haven't used it that way doesn't mean it doesn't exist. Perhaps you should curate your feeds a bit better.
I would argue that the immediacy of information comes at the cost of deliberation and the moderation that encourages. I'm not sure the result is a net gain.