I live under singlepayer health care. I like it, but it does have its downsides. For example, let's say you have something really severe going on, and you'd like to try a hail Mary. Well, you can't, as the only treatments that are available to you are whatever treatments have been deemed effective and reasonably safe by the regulatory agency. Experimentation, in lack of a better word, is a no-go.
I never experienced this as a problem myself, but I can easily imagine that someone could.
So I think the best is to have single payer available to everyone, but with private for profit doctors available if you need or want something a little more unorthodox and you have the means to pay for it.
EDIT: Seeing as I may have come off as a bit gloomy, I think I should list why I wouldn't want it any other way.
- My dad had cancer. Chemo and everything covered.
- My kid broke his arm this spring. The only expense was me buying a sandwich while they inserted a titanium rod into his arm.
- Same kid has ADHD. I can show up to any pharmacy in the country and fetch his meds (stock pending) without paying anything.
- His brother also has ADHD and poor eyesight on one eye. Meds and glasses covered.
- All of my kids were born in a hospital at no expense.
- I didn't learn until last year what the hell "copay" is, and the more I learn about it, the more thankful I am that it's not something I have to think about.