The real problem is that individually-purchased health insurance is more expensive (or unavailable). While public health care is one solution, it's far from the only solution.
An alternate solution would be to end the favorable treatment of employer-provided health insurance. Once everyone is purchasing their own insurance we will have a reasonably functional market, as we do with auto, homeowner's, and life insurance.
Having been involved in picking health plans for my startup, I am not optimistic. It was a giant pain in the ass. The number of variables seems much larger than car insurance, and the consequences murkier and more severe.
Choice is good. If the number of variables + consequences are too much for you deal with, then there's market opporunity for a startup there.
I agree with parents' feeling that were the regs to be fixed (or a new regulation enacted that stopped this bundling) a better market (as exists in car insurance etc) would develop.
Choice is in fact not an intrinsic good. Read The Tyranny of Choice for more on why.
It's especially not good in cases where the feedback loops are long and highly variable in outcome. Humans are very good at optimizing frequent choices with readily visible consequences, but are terrible otherwise.
An alternate solution would be to end the favorable treatment of employer-provided health insurance. Once everyone is purchasing their own insurance we will have a reasonably functional market, as we do with auto, homeowner's, and life insurance.