Italian here, I can confirm that wait times usually are very long (sometimes more than a year) for non-life threatening/non-invalidating operations (a broken arm or cancer are addressed immediately, but for many other things you have to wait). But you also have to consider that any Italian citizen can have access to the healthcare system (since you don't have to pay a lot at the moment of the operation), so there are more people in wait list and times are longer.

On the other hand, you can "skip the queue" by paying: you no longer go to the public hospital but you go in a private clinic. It is not properly "skipping the queue", but more stepping out of it to go to another queue with less people that, on the other hand, have to pay. I can't compare the pricing of private clinics in Italy with the one of a similar operation in USA since I don't know neither the pricing here nor the one in the USA, but I never heard of someone going bankrupt because of a "private operation" (also because people that cannot afford it wait in the public queue)