Besides exploiting taxpayers by irresponsible individuals, there's another moment here that even introducing commercial insurance can't fully eliminate. That, as someone already said, GRS members risk health and life.
True, with commercial insurance there are immediately fewer such cases, because people are more cautious, since the insurer can refuse the claim. But accidents still happen. Except in obvious cases, it's often hard to assess if the mountaineer was prepared for the tour, not just equipment but also knowledge, experience,... whether the accident was due to negligence or really bad luck, whether the mountaineer was careful or not, what was going on in his head,... Here individual consciousness is still needed. Not out of pity for insurers who profit from accidents anyway, but as said, for the rescuers themselves.
I read a story of one of our mountaineers who climbed a high mountain in the USA, I don't remember where. In the hut below it, the local ranger checked him from head to toe, checked the equipment, verified if he knew how to use it, checked experience,... Then he said: "Yes sir, USA are basically free, everyone can go where they want (except private land), do what they want but so as not to endanger others. I don't let just anyone up the mountain because if something happens to you up there, it would endanger my guys and their lives when they come to rescue you."
And probably regardless of who would pay the costs of the action...