We have a state system in Uruguay too, and it's amazingly better than the one in the U.S. as well.
One difference, I think, is that it reduces the imbalance of power between consumers and providers. The state can and does force prices down.
It sucks if you want the absolute best healthcare, but you can get that by paying (it's not forbidden), but the healthcare we do get is "good enough".
It's also lacking in preventive medicine, quality of life and cosmetic, but I'll take that over the U.S. system anytime.
We have private emergency systems, and they work extremely well for the consumer, my girlfriend had a burn from scalding water and was treated by a doctor within 5 minutes, for U$ 15. Doctors at those emergency services are criminally underpaid, though (as little as U$ 500 per 6 hour-shift monthly)