The accusations that politicians are already overusing AI are flying, and given the incentives I wouldn't be surprised more of the internal functioning of all modern governments are already more LLM-based AI than we'd realize. Or particularly appreciate.
By that I don't mean necessarily the nominal function of the government; I doubt the IRS is heavily LLM-based for evaluating tax forms, mostly because the pre-LLM heuristics and "what we used to call AI" are probably still much better and certainly much cheaper than any sort of "throw an LLM at the problem" could be. But I wouldn't be surprised that the amount of internal communication, whitepapers, policy drafts and statements, etc. by mass is probably already at least 1/3rd LLM-generated.
(Heck, even on Reddit I'm really starting to become weary of the posts that are clearly "Hey, AI, I'm releasing this app with these three features, please blast that out into a 15-paragraph description of it that includes lots of emojis and also describes in a general sense why performance and security are good things." and if anything the incentives slightly mitigate against that as the general commenter base is starting to get pretty frosty about this. How much more popular it must be where nobody will call you out on it and everybody is pretty anxious to figure out how to offload the torrent-of-words portion of their job onto machines.)