Maybe you think that the place where things don't work is Italy, and just Italy. It's not true!
A disclaimer: I live in Hessen, and I don't know how much of this applies to the rest of Germany.
Here, if you are too rich, you can't be insured by the state (actually, by any public health insurance company. There are more ones). It makes sense that you pay it for yourself. But... hey, even if you're not so rich, you pay something to the state for it. If you are very poor, obviously, you pay very little (or nothing). If you are middle-class, you pay also for the poor people (and this already doesn't make sense - the money for the poor people should come from taxes paid by everybody). If you are very rich, then you go to a separate system, and there you pay just for yourself. Actually, it turns out that rich people are less often ill, since they have more comfortable lives (obviously, on average). So they pay less. While middle class people have to pay a lot because they pay for poor people. OK, that's fucked up!
Actually, this part is worse than in Italy. Sometimes, when I'm in other country, I realize that while the Italian state does work worse than other states, we sometimes tend to exaggerate the perception of this, and we, the Italians, feel so bad about it.
It's like when you need group therapy: you think your situation is very bad and unique, but knowing other people with a similar problem allows you to see that after all, you're not alone. That's why the community of the Italian people, as a whole, need group therapy. IMHO. Well, if you can talk about the community of the Italian people... we don't really want, quite often, to be a community.
Note: the first part of the analysis (on German health system) is not mine, I'm republishing it for the benefit of the public. And it was explained me by German people, so I guess it's trustworthy enough.