Benefits of the higher income equality are mostly social, not economical. It's unclear that a society with some sort of income redistribution is going to be better off economically in the short term. In the long term, the value of human capital coming from the lower income strata could benefit the society. Also, to quote my friend, a bona-fide billionaire, "Income inequality will eventually lead to stratification and exclusive groups suck in the long run. Look at the royalty in Europe - if you keep fucking around the same tiny gene pool, nothing good will come out of it"
I hate to tell you, but that's a myth. My former boss, RIP, once said a long drunken rant about a persons trajectory in life. It's is akin an expected value of a stock at time T, he said. There is a spot price (i.e. what you are you born with, money, family etc), the forward drift expectation (two variables there, the quality of the society and your personal hard work) and then there is volatility around those variables (which we commonly know as luck). If you are born into riches (high spot), it does not take too much work to keep afloat. If you are born into rags (low spot), no amount of work will get you to proper riches without a stroke of good luck.