I'm sadly aware of how ridiculous the insurance situation is. In our current legal (and legislative) environment, the fact that we don't have firm tort limits is problematic. It means that doctors who might be accused of malpractice either will do so flagrantly, or refuse to act without massive barriers (provided, of course, by the insurance companies). There are a lot of things that need to change to upset it and I think any of them would be valuable.

Reduce the public financial aid availability - schools will lower their tuition costs and fees eventually, or they'll find themselves with far less students. That way, doctors & lawyers don't end up saddled with a lifetime's worth of education debt (and side benefit - neither does anybody else).

Instate firm lifetime tort limits, so that a doctor (who's already saddled with debt) doesn't have to fear for his career with every patient. That will sharply lower insurance loss rates and payouts, which should impact premiums. Less fear for doctors, less work for lawyers, less work for actuaries.

Those two broad changes alone would fix a lot of issues.

If you do need some form of public insurance, don't insure the patients. Everyone is a patient, supporting them might not pay back. Instead, set up a government funded malpractice insurance fund for all medical (dental/psych/etc) doctors. That encourages more people to become doctors, sets a de facto limit on the insurance plan and premium, and supports the skilled and educated people we actually want.