It is likely that single paying would be provide lower cost then what we pay today, I think it is highly unlikely it would result in better care. For example in many places in the EU semiprivate rooms are only for those Rich people that pay for their care, the "free" sick people are put in "efficient" open-plan hospital ward with many more people

Also there would be a huge drop in medical research, in addition to government regulation driving up costs, the US Health System more or less carries the rest of the world for R&D, companies charge the US exorbitantly because in the rest of the world there are price controls, once they stop being able to exploit the US Health Consumer because we also have price controls they will simply stop or slow their R&D to safer avenues and take less risks..

There are also 1000's of other reason why a US Universal Healthcare system will be vastly different than any thing any other nation has tried.

One big one is our obesity problem, once we have Universal Healthcare, are you then going to support Universal Diets, and Universal/Mandatory Exercise??

I would add a tax onto activities that increase healthcare costs, yes. I'm not stopping your from doing it, I'm just bringing the externality into the equation.

If you speed, we ticket you. If you speed too much, we raise the price of your insurance. And so on. This is no different. Risks have costs, and you pay for the risk you create (when a choice is provided).