The problem is that insurance products you can buy don't cover that risk (and people have to rely on other dodges to keep their premiums reasonable, like insurance pooling) — and that's market failure.
That's a BS solution, you don't shop around when you need emergency medial treatment, because you're in the middle of a medical emergency. You might not even be conscious.
And lets say you're a weirdo who spent hours researching ahead of time, chose the "best" ER, and etched your choice onto one of those medical alert bracelets. That does you no good when you're away from home, or even just across town.
Yeah, there are certain cases where market-based healthcare reforms could probably do a lot of good (especially around outpatient and elective stuff), but "the market" and "letting the market work" are not the solution to all problems.