I specifically focused on the standard of living of the poorest %20.

"income inequality" presumes that everyone should make the same amount of money. This is silly, and the only way to achieve it is to have absolutely everyone be poor.

The overall total wealth of the country, and the standard of living of the lowest %20 goes up more when you allow for capitalism.

There are no excesses in unregulated capitalism that I've seen because there is no unregulated capitalist country. The extensive "documentation" you refer to, that I have seen have been essentially easily refuted propaganda.

I do not doubt that there are a lot of people who wish to see society absolutely controlled, such that nobody is richer than them. But in doing so, they make everyone poorer.