I would like to address the original post and analogy to the medical profession. Licensed professions have a profound affect on the public, whether it is Engineering, Medical, Flight, or whatever they are on a different level of responsibility than diving, rock climbing, and other higher risk hobbies. The assumption made by the OP is that diving certification meets this same level of training, expertise, and duty to the public. This is a bad assumption.
The liability comes back to the individual when it comes to diving. The student takes some risk, the instructor takes some risk, and the shop takes some risk. However, the agency will not, and the OP's question is why. The certification issued by the agency only allows the instructor to use the agencies material and standards. It does not provide a license to teach. In fact, anyone can teach someone to dive (I don't recommend it), but this is true, there is no law that prevents it. There are laws that prevent Engineers, Medical, and Flight personnel from practicing without a license.
The instructor takes on the risk of teaching and this is why most courts come back to the instructor for liability. If the instructor can demonstrate that the shop caused the instructor to do something that increased that risk then the courts will find that the shop has liability. The problem with the OP's intent is that it is very difficult for the instructor or shop to demonstrate how the certifying agency had any role in the action that caused harm. They would need to show how the training material was flawed to cause harm. This is highly unlikely due to agency attorneys review of material before issuing.
Do we have bad instructors, some, yes. Do we have good instructors, most, yes. The problem is educating new students the difference. Most new students believe that their instructor is licensed, as we discussed above, this is just not true. I don't advocate for licensure, but we need to educate the public of this fact. If we could, I believe the public would weed out bad instructor and bad shops. Can the agencies help with this? Yes, but it is not in their financial interest to do so. Can the shops help with this? Same answer. I know SB says it all the time, find a good instructor! How do we get this word out to the public? That I believe is the real question!