The only long wait times in socialized health care are for non-critical issues, although sometimes the definition of "non-critical" can differ from what a person might expect.

I was a long term pain patient because my spine has been fucked since i was a teen, and waiting times for things like these are sometimes longer than they should be. But every time i had an emergency, service was impeccable and on par with the highest level of care you can pay for.