Sewer works coz you could have a private system of sewer as well. Whatever you got the point.
In France, drugs costing the most to our social system are those related to elder disease, such as rheumatoid arthritis, AMD, etc.. which touch pretty much every one one day or another.
Most of people are responsible : they don't go for no reason. Most of people knows the system is "fragile" especially since people are living longer and longer and so being more sick.
But even if some people would feel spoiled because they pay without ever being sick (even if there is a serious bias in this since people tend to minimize to themself their health trouble), you just don't think that way when you live under free healthcare.
It will not be the case at start if one day you go into that path yourself, because you knew how it was before, but your children will not wonder about that.
It's like if you are saying "well I breath less than other people, because my lung are in better shape/I'm smaller/whatever, I should have a discount on taxes about ecology" people don't think that way, because when you need to breath, you breath. And people breathing more than other don't get seriously charged for breathing too much.
Why? Because we are used to breath "for free" (even if we pay some taxes about air cleaning and stuff).
Here is the same, that's just a state of mind.