Single payer systems are popular and work well, but you are right that it is not the only solution. Countries like Germany use heavy regulation to manage the healthcare system. However, I don't think Americans would accept this level of "government interference".
They already have that level of government interference, just not in the right way.
That is the bizarre part of the US system - it might very well work better than today if it was actually a free market, but they've managed to get the worst of both: A highly regulated market where the regulations doesn't ensure proper service.
