This is where the price of being a free society means dealing with unpleasant choices. Once we start saying we need to make an exception for X, whether X be children, the disabled, or blond guys named Jeff, we start further complicating already difficult matters. As Lissa so rightly points out,
Children don’t have control over their situation nor the actions of their parents. Is it fair to let children go hungry or without adequate medical care because their parents are too irresponsible to care for them?
which is a damned difficult question to answer. For a rich nation, for a nation that claims to care about all her citizens, allowing a child to suffer when the means to stop said suffering are readily available seems needlessly cruel and heartless. We have the ability to put a man on the moon, they say; why can't we feed all of our citizens?
The short answer is, because we are human beings, and human beings are venal, short-sighted creatures. While our capitalistic society make seem cold-hearted to those that have not, other societies fare no better in providing for all their citizens. Communist Russia saw lines for staples like toilet paper and light bulbs; North Koreans face food shortages; even our enlightened European brethren face civil unrest, riots, and unemployment. Simply taking more money away from those that earn it is not the answer; else communist nations would never starve; socialist nations wouldn't see their richest members receiving better medical care here in the USA than at home where it's free.
Unfortunately, it's a sliding scale. As Lissa mentions, the surest way to get more of something is to subsidize it; the quickest way to completely and utterly paralyze our medical system would be to remove the need to pay for any of it. Actions have consequences - as we start offering all sorts of "free" health "insurance", costs go up; hospitals close because they're unable to meet their budgets; doctors are squeezed out of their practices by skyrocketing malpractice costs. As more people swarm into the system with no thought of how it's being paid for, they're choking the very life out of the commodity they previously hailed as a "basic right".
Our system isn't perfect; even in our land of plenty folks go to bed hungry. People have to choose between food and medicine. Even worse, our lofty attempts to change this have failed miserably; the laughable "War on Poverty" has done little to end poverty but created a whole new type of second class citizen, a quasi-permanent dependent on governmental largesse. We have by large removed a great portion of incentive for whole groups of people to succeed, offering a mediocre albeit safe life that one need not get out of one's recliner to grasp.
There are hard, hard questions in all of this with no easy answers. For every action we take - offering "free" health care - we run into the law of unintended consequences - fewer and fewer medical students to become doctors in the future. We look to the quick fix - the handout to the family that's going hungry - and wind up with a monstrosity down the road - the welfare state that consumes and consumes, yet produces naught.
For every action there is an equal and opposite reaction. This is just as true in society as it is in physics.
That is all.