would drop significantly. You would be shocked at how much people would shop around though when money is on the line. Even for "emergencies" which only make up about 15% of healthcare costs, I would shop around before hand and know where I'm going to go in the case of an emergency. That is why insta-cares are becoming so popular. A great market solution to high emergency room costs for most items.
Of course sometimes time is more critical. And there will be good and bad insurers, but the beauty of today's technology is that it is so much easier to get reviews and general consensus of insurers. Overall costs would be so much cheaper that even if you occasionally got the shaft from an insurer you would still be way ahead fiscally.