While single payer is often a better system, it's not without its problems - in Canada ER wait times are ridiculous, my sister had to wait 10 hours recently and if you want to find a GP? Good luck. Everyone is booked solid.
I thought Obamacare seemed like a good compromise to be honest. Unfortunately it doesn't seem like that's been a miraculous solution. I think some sort of free market solution with a safety net on the low end could do the job, but I don't know what that would look like. And I don't think we've seen any proposals in that direction.
But right now I can see my family doctor with 1 day notice, most times same day, and they have someone on-call for phone 14 hours a day and on weekends. Mostly I can avoid ER and drop-in clinic visits completely.
Constrainted, non-infinite supply, basically infinite demand. What a great business to be in!