That's absolutly false bro.
First of all, if you want to get a private surgery to avoid waiting for the public, you're allowed.
You pay for that surgery and that's all. The post-surgery will be covered by the public that you're paying through taxes.
So you'll wait only if you don't have enough money to pay the private, what means that you wouldn't have money to pay the private wheter public wouldn't exist. So, now you have to wait but you'll have the surgery while if you wouldn't have the public system you'll have your surgery done never.
Second one.
If you'd have to wait 8 months (you won't, in Europe, a surgery like that is done in about 6 to 12 weeks) the public system will take care of everything you need until you get the surgery done (drugs, temporary prostheses, special transport, etc, etc) and the public employment service will pay you the same you received because of your work (because you're paying taxes while you're working).
As I said, it's as easy as choose people or money.