I think there's a real difference though when the cost is "baked in" via taxes or something else. If a doctor's visit has the potential to cost you hundreds or even thousands of dollars, unless something is really serious, chances are you're going to avoid going.

In a system where costs are paid through taxes, the disincentive to see a doctor is eliminated. That maybe has some negative effects (going to urgent care for relatively minor problems), but I think it has real benefits in terms of preventative care.

In terms of a countries overall finances, it balances out (not entirely - see my previous point), but in terms of affect on behaviour it has a huge effect (in addition to balancing out the burden that I mentioned before).