None of us can foresee all the results of our actions, not even within our own family or our own neighbourhood or business (I'm writing "family" rather than "one's own life" because I guess most of us do not really want a liberty that has a substantial risk of putting our kids on the street, lead to our partner being killed or maimed for life, acted upon them in the nick of time, without them or us (personally) having done anything much to get there or "deserve it"). No child, except the kid of a millionaire or a king, is born with the resources to take it safely up to adult life. We all depend on parents, schools, employment and on the community around us!
If we think all people must take "every consequence of what they do", then we shouldn't have any trouble with seeing unarmed men and women being raped, killed and tortured - or who see their children killed or forced into slavery - because they happened to live in a city that's taken by enemy forces (this was the regular thing in many places for most of written history, and still happens today in some parts of Africa). They could have moved out in time, or they could have declared they didn't want to have any part in the conflict, couldn't they?
Of course sometimes people make bad choices, they invest money in a poor way, your kids may start using drugs or people go into insane projects. But it would be nutty to presume that all kinds of misfortune are generated from willful choices, or that the one who makes the choice is most often the one who has to suffer. The banking crisis gives you sacks full of proof: the banks that are pulled down are not the ones who have made the most lousy transactions to begin with, but the ones where the crap ended up, because many kinds of business lead to secondary transactions, futures or insuring that can be very hard to break off.
So banks like Merrill Lynch end up with bad (and hastily written?) papers and obligations that represent business that was generated some place else. In theory, we should let all those fall, and Fannie and Freddie first of all, but in reality, that's not a path that you can take without breaking down society and worsening it all.
I do think there is a kidn of universal human right not to live in detitute onditions, not to have to die early or suffer unneeded, wasteful diseases. That's not to say that everyone has a right to free care at the most expensive clinics or that the presence of diseases is a negation of humanity. It's an expression of where we want to go.
Taxes? yes, you could make it voluntary to be joining or standing outside, but countries where basic health care insurances are fully voluntary (like the USA) invariably have a large chunk of people who are not able to get on the ladder (same with houses). The costs of actually getting an insurance may not always seem prohibitive, but the difficult part is getting the free money to ease past the bump in an existence where you're always scrounging, always pulling and squeezing to make ends meet somehow - with low wages or being on the dole, or no means at all.
It's no accident that poor people are the ones who get the really grave diseases; they don't have the money to go to regular health controls, to eat in a nourishing way or to see a doctor when something seems suspicious. Taxes are really the only way to get all on board - the state funds don't always have to carry the full costs but using taxes as a grounding for public health is the superior way to create an overall health care system.