The western world is already solving this, but not through letting LLMs prescribe (because that's a non-starter for liability reasons).
Instead, nurses and allied health professionals are getting prescribing rights in their fields (under doctors, but still it scales much better).
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.