There are already computer programs in place that assist doctors and nurses, like programs that check for drug interactions.
AI will probably get added to do things to assist practitioners instead of replacing them at first. A junior general doctor uses an AI as a diagnosis tool or a radiologist uses AI to help in diagnosing tumors.
Over time, costs go down the tools get better and you can use less time per doctor as the AI gets relied on to more of the grunt work and the doctor is just there to make sure nothing bad happens. By the time they propose outright replacing humans with AI, they are going to have a large body of evidence showing that AI has a better record than people.