@nony - To answer your question, I don’t think that societies can do what you’ve asked. This inequality, in my opinion, does not arise out of a concerted effort to skew income and wealth.
It’s not a conspiracy; it’s the result of decisions people make. Also, it should be pointed out that people who take a bigger piece of the pie have done so because they’ve made bigger sacrifices, and they also wind up paying the largest share of the taxes.
I’ve been in economic classes in college, but I have yet to see a so-called Lorenz curve for who pays the most in taxes. I guarantee you, it will be the people up in the top brackets.