A government agency governing what is acceptable speech is a bad idea.
This exists, and is called Wireless Emergency Alerts. Every phone sold in the U.S. today supports this out of the box.
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.
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.
Platforms that censor are going to win in the marketplace, because that’s what most people want in a discussion platform.