I recently picked up a prescription where the pharmacist said it would only cost $9 if I paid out of pocket with the Rite Aid discount card. Going through the insurance company would cost me $23. He said it had to do with the complexity of insurance company policies. I said, "no wonder so many people want single payer." The pharmacist agreed.
Conservatives tend to worry that single payer would mean less choice, but it seems like "choice" is mostly figuring out which insurance offering one wants while wading through fine print.
The most important choices, related to health, are things like lifestyle choices. What one eats, exercise and so forth. They don't talk much about that.
Some people say that less regulation can allow insurance companies to innovate and provide incentives, to their policy holders. Incentives for things like diet, exercise, free gym memberships and discounts for non smokers. There is some of this, but, in most cases, the insurance industry reduces cost by not providing coverage to folks with preexisting conditions. Less regulated insurance companies throw people off their rolls if they have preexisting conditions, or at least only offering them coverage at much higher rates.
According to a recent Diane Rehm show, around 130 million Americans have preexisting conditions! Wow. That's a lot of people. Almost half of the American people. I don't think the private insurance market can deal with all those preexisting conditions very well; especially low income people with preexisting conditions.