any sane person will choose a mix of the two

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.