I think we should recognize that if students (or qualified divers as well) were made to take out specific dive insurance then there wouldn’t be the recreational sport of scuba diving. I consider myself a responsible diver and therefore I took out DAN insurance for myself and my family, who all dive.
Also, and I’m only speaking for myself, I do not ever see myself, or my family trying to sue the dive professional who trained us. If I was unhappy with the level of training we received I would be having a conversation with the instructor intially, if that wasn’t successful then the dive shop and if I still wasn’t getting satisfaction then the certifying agency.