Yeah, but the work of lawyers has often forced industries to do things differently, even when the best science says they shouldn't do it that way. For example, lawsuits over botched baby deliveries that argued "you should have c[aesarean]-sectioned" resulted in extreme overuse of the procedure in the US, with higher resultant risks.
I suspect the reasons for increased c-sections are manifold.
When we medicalise pregnancy and childbirth, then fill hospitals with profit driven policy, and surgeons who fear malpractice accusations, is it any wonder c-sections can become over used?
Fear of malpractice alone can’t explain it all, as it some other lawyer could demonstrate c-sections are over used and lead to complications.
So ... I wish it worked like you described.