I'm not suggesting Beehaw/etc should be government funded. Rather I'm suggesting it's already possible for basically anyone in the fediverse to report a post as needing urgent moderator attention.
I think there will be tax payer funded efforts, donation funded efforts, volunteers, etc that are unaffiliated with any specific instance but go through major instances and hit the report button where they consider it to be appropriate — not just manually with people but also with automated tools such as searching for images by a hash of their contents or maybe even running messages through a Large Language Model to check if it is, for example, a form of targeted harassment.
And yes, the report feature will be abused. That's unavoidable and needs to be taken into account when deciding how to respond to a report. An algorithm could easily prioritise reports based on the history of past reports made by the same person / organisation.
Stack Exchange has a pretty good system - decisions by individuals are not trusted. Rather those trigger a review by a randomly selected (and trusted) individual to get a second opinion. And even after a decision has been made and an action has been taken (ban a user, etc) there's often a third or even fourth review. And there are processes to appeal and question decisions.
It's not an easy problem to solve, but as the creator of mastodon said - many hands make light work. The fediverse can some day have a billion people doing moderation tasks - where even simple acts like hitting the upvote button become part of the moderation system (upvote would imply that this account holder tends to make valuable contributions to the community, and should make the moderation system less likely to come down with a ban hammer).
And I also think there is scope for some communities to be entirely government funded. For example I'd love for every city in the world to run an offical community, with official local government anouncements as well as moderated discussions relevant to people who live in or are visiting the city.