> you envision a future where there will be say a hospital, ran by anthropic which is AI powered fully, no company behind it, just plain Claude running everything from the moment you walk in till you walk out

Everything as much as possible, yes, and the company behind it will be an AI driven autonomous corporation as well. Although I suspect that by then there will be some industry specific AI model being used by hospitals, not just plain Claude.

AI will handle patient data, diagnostics, prescriptions, everything that doesn't absolutely require a human and can't yet be done by a robot.

Somewhere, some human will be making money but they will be far from any legal liability, probably safely ensconced in a bunker on a private island when the gravy train really hits the fan.

>I am having a hard time imagining a future where “AI” isn’t just a tool that a given establishment decided to use much like anything else they use

The people making the decisions, investing the money and writing the laws imagine so much more, though. You assume the future of AI is governed by rational people making rational decisions but it isn't, it's governed by Musk and Thiel and sociopaths and grifters and cultists who want to immanentize the eschaton so they can stand at the right hand of God.