I'm pretty sure that in "socialized medicine" countries i.e. the rest of the civilized world pretty much, they also "do everything" even if chances are low. AND everyone involved (including family) can do their part in it without having to deal with papers, money, bills, proof of insurance, and the plethora of other likely speed bumps that exist in the US.
So no, I don't think that's why. If anything, the amount and quality of average care for the average US citizen is lower, if life expectancy and my anecdotal observation are valid indicators.
It's expensive because it's a business designed to make profit every step of the way, and over time has created many steps to feed.