Doctors might answer that no cases would be averted. They might say that our legal system has created an atmosphere in which accepting responsibility for a medical mistake and apologizing only guarantees a lawsuit.
I don't think so. I can't even count how many clients over the years have told me 1) that they have no interest in suing thier doctor, or any doctor; but 2) that they are so frustrated by a doctor's defensiveness, or downright disappearance, after something went wrong that they are motivated to explore a legal solution.
My experience with doctors is that many are honest and caring individuals. But even the most honest doctors often feel that they must conceal mistakes in order to avoid the legal system. Few consider that most patients, even those who are harmed through a medical mistake, want to avoid lawyers and the legal system as much as they do.
Many doctors would be surprised to learn that acceptance of responsibility sooner often avoids the need to deal with the legal system later altogether.