A friend of mine ran across this in Switzerland. It has a nominally free-market system, but when he moved there, he ended up automatically enrolled in a plan without doing anything at all. He was remiss in reading and translating all his mail upon moving there, and after some months of inaction: 1) he was signed up to a default insurance plan; 2) which was partially subsidized based on his estimated income; and 3) he was billed for the remainder. Nominally private-sector, but still quite state-supervised. There is a minimum standard for plans, you must have one, and subsidies ensure that everyone can afford it. Unlike Obamacare, the "must have one" part is not enforced by fining you $700 on your taxes, either, but rather by actually signing you up for one.

This is how vehicle liability insurance works in Sweden. You must have it, and if you don't, the government will just sign you up for a government-run default insurance pool and bill you for it. Certainly beats having to have "uninsured motorist insurance"...

Is there a practical difference between being billed for a plan you were automatically signed up for and being assessed a tax fine?

Well, in the first case you're actually enrolled in a health-insurance plan, whereas in the second case you aren't. This solves many problems; for example, everyone who visits a doctor's office or hospital can be assumed to have insurance coverage, so those institutions aren't left with the mess of what to do with uninsured patients.

> But those systems tend to look like a "single-payer donkey with a free-market tail stuck on."

I wouldn't use either of the terms "single-payer" or "free-market" in describing systems in which there are multiple private sector health insurers (payers), and it is mandatory for individuals to purchase a plan from one, with highly regulated plan provisions and operations.

They don't much look like "single-payer" anything, and don't very much look like any "free-market" bit has been stuck on (there is a market component, but its not free.)

> If that sounds exactly like the ACA, you're correct

The ACA is similar in outline, but the differences aren't particularly subtle (the ACA's isn't universal; the poor, elderly, and disabled -- rather than being subject to the mandate and operating through the same market, potentially with a public subsidy, instead are directed to one [in some cases, both] of two completely separate public insurance systems, etc., etc., etc.)