I wouldn't bank on free markets fixing emergency room problems. While anecdotally some parents may choose to take their children to one hospital or another, I doubt this is a statistical norm. I imagine most people choose the nearest emergency room for most emergencies, and hold off for an appointment with a doctor otherwise. Sometimes, it's just a baby with colic. But sometimes (increasingly in a country with a serious obesity problem) it's a heart attack, and no one is going to drive their dad 45 minutes to the cheap hospital when the one that will save his life is 10 minutes away. Because of this I don't think hospitals have any incentive to drive down ER costs.
But maybe I'm projecting, since my experience with ERs tends to be "Oh shit... get me to a hospital now Google Maps" rather than "I should Yelp some reviews of hospitals, because I have time."