If patients had an option - a la you can get an appointment now with an external consultant for $X, or wait two weeks - then that would make sense. But instead you pay for health insurance to literally insure against catastrophically expensive health-care costs (that's the point of insurance - "socialize" risk so that the individual doesn't get "wiped out" in case of an extraordinary event), yet you may still go bankrupt even if you do everything right!
Also, most other countries have a two-tiered system. Public health insurance, possibly worse and slower (don't necessarily agree), or you pay extra for private health insurance and get nicer hospital suits, better doctors and short wait times.