but in general, proponents (like myself) of "single payer" systems of health care delivery reject the "free market" approach.
There are a variety of "single payer" systems - some are nationalized, like the NHS in the UK - and receive at least a percentage of their funding through contributions made by workers and employers (a "tax", if you will, like FICA or Medicare, but not exactly the same). Some are a combination of nationalized service and health insurance - the big difference being that the insurance is strictly regulated and required to be not-for-profit at the base level.
All of these systems allow for the purchase of additional insurance to cover things that are not covered by the system (cosmetic surgery, for example, or private hospital rooms - bells and whistles, basically). If someone has enough money, they can opt out of some of these systems and use private insurance . . . but honestly, even most very wealthy people don't see the point of doing that.
Essentially, "single payer" systems are "free at the point of service" - in other words, if you go to the doctor you do not pay a deductible/co-pay. You ARE paying, of course - but your payment was made through your contribution to the general fund through your "tax".
So, if you wind up in the ER with a broken leg, you're not going to have to fill out paperwork proving your insurance coverage or receive a bill for the percentage the insurance didn't cover.
Is it perfect? No. Every variety of "single payer" has drawbacks - but in comparison to the cobbled together mess of out-of-control costs that make up (and will continue to make up, because the ACA doesn't address costs) that we have, "single payer" looks like paradise.
And we still just have our noses pressed to the glass, looking in at what we cannot have.