From real world experience as a patient that has had a lot go wrong over the last decade. The problem isn’t lack of automation, it’s structural issues affecting cost.
Just as one example a chest CT would’ve cost $450 if done cash. It costed an insurer over $1200 done via insurance. And that was after multiple appeals and reviews involving time from people at the insurance company and the providers office including the doctor himself. The low hanging fruit in American healthcare costs is the stuff like that.
Calling that "low hanging fruit" isn't accurate, because entrenched and powerful interests benefit from it being kept that way. That extra $750 is valuable to the capitalist that gets it. The jobs to process those appeals and reviews are valuable to the employees who do them. Deleting all of this overnight will fuck these people over to varying degrees, and it could even have macroeconomic implications.
With that said, although it will not be easy, this shit needs to change. Health care in the United States is unacceptably expensive and of poorer quality than it needs to be.