Surely it would not solve every source of human misery, but I don't see how it wouldn't be a substantial improvement.
> I doubt it would be an easy sell to suggest sharing the fruits of everyone's labour regardless of the amount of work each person has put into producing those fruits.
There is a whole branch of political philosophy dedicated to exactly that, which capitalists around the world (valuing utmost the ability to accrue and hoarde capital) have spent over a century turning into a dirty word.
Nowadays in the US, even the suggestion of public healthcare is an untouchable evil, because helping your fellow man is seen as being taken advantage of, and the idea that someone might get something for free is abhorrent. This, despite that fact that public healthcare is normal, successful, and more efficient in almost all other western democracies (because the cost of services isn't padded by executive bonuses and investor returns)
Besides, if you have insurance, you already believe in that general concept. It is a pooling of resources with the knowledge that some may give and take in unequal measures, but that on average less people will need to take than will give, and that you have a safety net in the case of an extreme unlucky event. Same idea, just applied on a societal scale.