In the case of mandating healthcare, it's not that I think people should have the choice of whether or not to participate in the system, it's just that the rest of us can't go on just letting our fellow citizens die when they get severely injured. It's just unthinkable.
Also, I think this debate is a rabbit hole since it is a complete strawman. I would argue that, given the correct subsidies by the government and proper knowledge about health care, almost every person in the world would choose to buy a health plan of some sort. If you don't agree with that, you must have a strange view about how the vast majority of people make decisions.
I certainly agree with that, and the thing that is going to help us get to a system like that is a mandated system. Do you also think social security should be optional and when people get old and can't work they are SOL and left to rot?