The medical industry relies on scarcity and it's also heavily regulated, with expensive liability insurance, strong privacy rules, and a parallel subculture of fierce negligence lawyers who chase payouts very aggressively.
There is zero chance LLMs will just stroll into this space with "Kinda sorta mostly right" answers, even with external verification.
Doctors will absolutely resist this, because it means the impending end of their careers. Insurers don't care about cost savings because insurers and care providers are often the same company.
Of course true AGI will eventually - probably quite soon - become better at doctoring than many doctors are.
But that doesn't mean the tech will be rolled out to the public without a lot of drama, friction, mistakes, deaths, and traumatic change.