Ayn Rand's advocacy of self-interest above all other considerations is absolutely right, IF you only care about fairness. If fairness is our only metric, then a pure capitalist system would be close to optimal. There is still the matter of rent-seeking behavior, but that is another discussion. The problem is, for most people, fairness cannot be the only metric. Some people are just worthless, and they deserve nothing. But we should give to them anyway, because people's fates, and character, are not entirely self-determined. Ayn Rand tries to gloss over this, but it's true, especially for children. Strictly speaking it is unfair and unjust to give to these people. But who cares? I don't want anyone to be homeless even if they deserve it. On the other hand fairness and justice does matter. It's just as much of a travesty, in my opinion, to make value created count for nothing. The person that provides more value to humanity should be rewarded in proportion to the value created for others. In capitalism, that ideal is realized much closer than in socialism. So any sane person will choose a mix of the two. And that is what we do. Then we squabble over the exact mix.
I think we agree that capitalism does a good (but not perfect) job of allocating resources to where they are most useful, and providing incentive for people who are good at creating things people value to create a lot of those things. What about the gaps? You allude to the awkward distinction between the deserving poor and the undeserving poor, the latter sometimes considered a myth. In the abstract, I find it hard to say there are people don't deserve help, though with limited resources I would want to help people who seem to have bad luck before those who have a history self-destruction. Some people have difficult family members who exhaust everyone's patience, who would use additional financial support to dig themselves into a deeper hole. Perhaps the best you can do is try to ensure that basics like shelter and food are available. At the same time, some people provoke us into debating capital punishment, so it's not a guarantee that simply being a human gives you a claim to compassion and aid. While we haven't found any better way to create and distribute wealth than capitalism, there are alternatives to reducing the gaps other than "socialist" redistribution programs. Charity is the most conspicuous example, and like public welfare programs it won't be completely effective. People can skim and get rich from an organization like the Red Cross, but its budget depends on keeping a good reputation, while a government program is more likey to continue business as usual even when opportunists find ways to profit from the guaranteed cash flows.any sane person will choose a mix of the two