The laws around medical malpractice don't fix it when doctors screw up, but they make it a lot less likely for the screw-ups to happen, since those laws force doctors to adopt reasonable standards of care.
To me what you are describing is basically regulations. Personal accountability only derives from regulations because there are punishments, in that case it aligns incentives.
Regulations are only one form of personal accountability. Regulations, in theory, create uniformity and transparency. These can be good things. In practice, regulations are often selectively enforced, which leads back to the same situation as in a dictatorship, but with a formalized process of input for the dictator.
I actually disagree with you that malpractice lawsuits are examples of regulation. More often, when something goes wrong and a doctor is involved, there is an argument about whether the doctor was negligent or not. There is no fixed "standard of care" that is written down, only a set of practices that are known throughout the industry. Experts argue about whether negligence occurred or not. There are regulations that the experts can cite in their determination of negligence (some of those rules carry separate penalties too), but you don't need to have broken any rules to commit malpractice. This is a prime example of accountability without regulation.