I feel kinda guilty posting in here on the issue of health care as a Canadian, because I don't want to come off as gloating, but I just want to affirm some of the things that are beneficial in a "single-payer" system (that specific terminology isn't used here, we generally refer to our system as "universal healthcare").
I have never heard of anyone being refused care because they were not "covered," and I have never heard of anyone not being able to afford treatment or surgery.
Dental and vision are not covered publicly, they are out of pocket, many jobs do offer employees dental/vision plans.
Medication is heavily subsidized but not free. I'd occasionally pick up medication for my grandparents/parents, stuff like arthritis or blood pressure meds, and they come to $2-$3 dollars to fill.
There is a big problem with medication and it's the subject the occasional national story. Sometimes, a person has a rare illness and it can only be treated by a drug that is manufactured solely in the US or abroad, and if it's experimental and not recognized in Canada, or is suddenly "delisted" in Canada, then it can cost Canadians tens or hundreds of thousands of dollars. Of course it's the same for Americans, but it's jarring for Canadians to see someone having to mortgage their home or set up crowdfunding for their meds.
Wait times vary from a week+ to see a specialist to a couple of months for surgery or an MRI. Seeing a GP or going to emerg can have you get an initial diagnosis and referral or emergency treatment/surgery withing hours though. Those are my personal experiences for myself and my family.
I don't know anyone that wants a private system. We have wait times and a crowded system, but that's not a function of health care being tax funded, that's a function of there being more people needed care than people providing care, and there's always going to be a gap because there are only so many people capable of providing care because of the high high standards for being a medical professional. You can't hire doctors like they're low-skill labour.
Plus there are other procedures that are limited because of scarcity. If you're on dialysis and need a kidney, well, all the money in the world isn't gonna make a kidney just show up.
All private insurance would do is kick low, and eventually middle-income people to the back of the line for surgery and transplants as the rich people buy their way into the operating theatre, and most people are aware enough to realise that they'll end up on the short end of the stick.