The issue with that is if America gets the military might to kill the world, why wouldn't they just conquer it instead?

Unless your saying it's just the rich/powerful of America, and the lower classes in America will also be getting it.

In which case, while it might not suffer from the logistics, cooperation and government issues, it does however concentrate the issue into one nation for the most part. Meaning any nation with undisclosed/secretive nukes like Israel could impose M.A.D. on America and threatening nuclear war if they just start Mass killing/conquering their way throughout the globe.

Moreover, when it's specifically America, I can't see them making enough headway into specifically China to successfully subvert them enough to render the threat of their nuclear stockpile null and void. Mostly, and ironically, due to this authoritarian construction and the lack of probable willingness for Xi to give up his throne to make his life slightly better, if not stay the same or even cause him to lose some power due to being one of a bunch rather than a sole authoritarian tyrant with his own kingdom.

Of course an AGI might get anti- nukes tech...but I don't see how that could happen without WW3 breaking out shortly after.

Overall, it has better odds in general when concentrated on America, but runs into an even more immovable roadblock than the rich illuminati route.

And America is presently suffering from outbreaks of eugenicist rhetoric, actual neonazi movements, kleptocracy.

And America is home to by the three most successful AI-development teams (Google, OpenAI, Microsoft).

And America is already working on enormous offensive drone swarms

Not that drone swarms are by any means the only tool they could use.