>So for example, there's a thing going around Facebook with Jimmy Kimmel about healthcare, which has everyone saying that no one should never need to consider finances when their child is sick. This is plainly false in the general case, because it would imply infinite resources. In the real world, there will always be a point at which we must say "no more".

That's not "plainly" false, unless you know some medical treatments that cost an infinite amount of money to perform. If we assume that less than 1% of patients are catastrophically expensive, then based on actual data it looks like dropping them all would save less than 20% of total spending, possibly a lot less.