" Moreover, it introduces a risk that medical decisions get overridden by polical ones."

This is exactly what is happening now when the insurance lobby owns the congress.
The political decisions are being bought and the medical decisions now take a back seat.
The CEO stand between the doctor and the patient. You can still pay and pay and not
get served with a private insurer.

NHS in other countries are not overriding medical decisions through politics. Only in the US where lobbyists control the doctors. Big Pharma and the AMA are examples.