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).

You are right that you also have to include taxes, but you also have to account for the fact that taxes are dependent on income and coverage is always guaranteed. So it is not the same as paying for a service. It is something else.