"Better machine alternatives" implies that the police and military aren't first and foremost evaluated through their loyalty. A powerful army that doesn't listen to you is not a "better" one for your purposes. The same isn't true of the economy: one could argue that our current economic system is beyond any one person's ken, but even if I don't understand how my coffee came to me and no one person would be an expert on that entire pipeline it works.
The idea that AI could lead to power concentrating in the hands of a few oligarchs who use a robot army as a more effective version of the janissaries or praetorian guard of the past certainly seems broadly plausible, although I'm not sure that the effectiveness of the Stasi is the limiting factor on autocracy or oligarchy. I don't understand how that links to human extinction. For most of human history, most people have been unable to meaningfully impact the way their society operates. That is responsible for an incalculable amount of suffering, and it's not a threat to be taken lightly, but if anything one might argue it's likely to ensure some human survival for longer than a less stable, freer system.