Non-essential surgeries tend to have longer wait times (such as hip replacements in elderly people), but conversely, essential care is accessible to everyone at no cost and in a timely manner.
I live in Canada, and recently had appendicitis. My appendix was removed less than 24 hours after symptoms began, and 10-12 hours after I arrived at the hospital. I walked in to the ER (after a very painful car ride), they asked me some questions and gave them my health card, they said how much, I said 7, they did blood tests and I had a CT scan, I waited a few hours, and then I was wheeled up to the operating room, after which I spent the night in the hospital and discharged the following morning. Not once did the question of insurance or payment come up, and I even had a private room after the surgery.