A government agency governing what is acceptable speech is a bad idea.
The draw of the twitter-like approach is that the government messages are a portion of an existing stream of communication that people are already using/consuming.
This exists, and is called Wireless Emergency Alerts. Every phone sold in the U.S. today supports this out of the box.
Blog post here: https://dynamorando.pages.dev/blog/the-public-web/
The most common refrain that I get whenever this topic comes up is "First Amendment" - meaning that public funded social media should not be in the business of moderation; though I often wonder how come NPR, PBS, BBC and so on don't run their own social media websites (based on your deciding flavor of ActivityPub instances.)
I believe the German and Dutch governments run their own Mastodon instances, I don't understand at the moment why other governments don't follow this path.
You work for who pays you.
Platforms that censor are going to win in the marketplace, because that’s what most people want in a discussion platform.