Why should I have to pay for their lack of responsibility?
Because "Herd Immunity," that's why. As those "irresponsible schmucks" begin to die, they don't just switch off like a lightbulb. As their bodies' defenses begin to fail, various infectious diseases of one kind or another set up shop in their bodies and begin cranking out one communicable illness after another. Don't think of that guy with the failing liver as just some alkie getting what he deserves. Think of him instead as the walking tuberculosis distributor who breathes the same air you do. As much as you might want to think of yourself as some rugged individualist, the awful fact is that you are part of a big old herd of people, and the health of the herd eventually becomes your health. See "Masque of the Red Death" for an illustration or look up "Mary Mallon" for an example of what your the hotel maid or the fast food cook you never even meet can do to you.
Of course, that's the ROI, self-interested, purely selfish argument I'm frankly sick of making. Let's pretend your health really was firewalled from everyone else. Let's suppose we're talking about some old drunk dying of richly deserved delerium tremens. Why should we give him anything?
We treat him not because he deserves it. We treat him because we're human beings. We treat him because we are a civilized people who do not simply stand by and watch while our fellow human beings die screaming. We treat him because there's NO religious or philosophical school of thought apart from monsters like Rand and Nietzsche that condones not treating him. You can't refuse to treat him and continue to call yourself a Christian, a Muslim, a Mormon, a Buddhist, or a Jew.
Oh God, I can already hear you whine, "But that's the role of private charity..." Apart from Tesla Museums, private charity is not how we get things done in this country. This is why we don't close down the VA in favor of the Red Cross. This is why our mail doesn't get delivered by a coalition of marathon runners. When We the People choose to act, we do so under the organizing principles of government.
Why should we have to pay for this? Well, mainly because you have a choice between putting patients in hospitals or walking over the highly infectious dying in the street. Because we as a society pay less by writing a few scrips than we do by trying to employ enough cops, prisons and CDC resources to handle the chaos caused by the desperate and dying.
But mainly because if you've ever actually seen another human being suffer and die -- and I don't mean Grandma passing in her sleep -- then you'd never even ask the question.