I think the above example illustrates why a malpractice insurance pool might be a bad idea. The one who makes the mistake must pay up. This will ensure those who make less mistakes will succeed at faster rate.
Do you also think the doctor who brilliantly saves someone's life should be rewarded the lifetime earnings of the person saved? Introduce "Value Based Pricing" in healthcare?
I think medical errors should be (financially and professionally) punished, but only up to some reasonable amount, aimed at the future and on damage to society, not on compensating the victim (which you can't really anyway).
If you want to be compensated in full for everything that might happen to you, then get personal insurance.
Getting insurance against i.e. disability is a better approach anyway, as this also covers cases where it is caused by no-one, by yourself or just by bad luck.
It seems strange that personal insurance is rarely mentioned as a (partial) solution for these situations in the US. Maybe because collective/social solutions have a bad reputation?
Value of something does not depend on the what the provider is providing but what are the alternatives for the consumers.
A brilliant doctor who saves someone's life should be awarded lifetime earnings of the person if the alternative is dying. Clearly people already spend a fortune getting state of art medical care for the same reason. Value depends on alternatives and not on what a doctor is doing.
Also a lot of medical errors are because doctors can get away with it or they have simply too high egos to go through a checklist. Penalizing doctors is important for their mistakes.
But I do agree to your point that there is no clear way of determining what is good compensation. Sometimes death destroys one life, disability destroys many lives. I think the jury must determine what the compensation is.
Social Security actually has some provision for disability. So we have a collective social system in place (I guess the payments aren't necessarily high enough to call it a solution).
I think people don't carry additional private policies mostly because they are spending most of their budget on other things and are somewhat short sighted.
