I doubt the claim of the commenter below who argues that it is malpractice insurance. There are by now plenty of “tort reform” states where malpractice payouts are capped. I would be very surprised if anesthesiology prices are any lower in those states.
The way to skip all of this is massive de-reg.
Also, education is closely tied with government funding, so it's impossible to bootstrap a college or university to cheapen the cost of education. Thus you can only go all-in to medschool. This is not 100% accurate, there are some alternatives like PA's and NP's. So the current system can absorb only so much.
There are also specific funding rules for residencies, which mean that the amount that is given is done based on gov funding.