Here's a place where the free market doesn't apply for the free market requires rational actors; there's nothing rational about getting hurt, passing out, and waking up in a hospital with a bill.

Here's some solutions, anyway:

Emergency centers close enough to each other that they must compete; you can then, if requiring further treatment, figure out the hospital of your choosing at your leisure.

Refusal to use any hospital for non-emergencies which does not offer competitive prices for emergencies; this pressures the hospital to offer better prices or sell off to whomever is.

Pre-determined prices paid in advance, mixed in a large pool of other people's advanced payments, to marginalize the cost of varying emergency service costs (i.e. insurance.)

Stop being careless about your health so you won't have to worry about it.

And of course, all of the above.