Not to mention, the only system I can think of where competition, which is what we're really talking about, was systematically eliminated was the USSR and other implementations of communism, which were both economically and socially a disaster. There's a lot of feel good stuff when we talk about fixing things, but the "thing" that needs to be fixed is sometimes a feature and not a bug.
The USSR is also a good example, especially with women's rights. There was a top-down equality decree without any sort of legitimate social movement. In practice, women in the USSR, outside of propaganda, were treated poorly and once the USSR fell, Russians just naturally fell into their deep patriarchal views which are mainstream there. If anything, women have it worse in modern Russia because of the USSR's heavy handed idealistic decrees.