There is nothing like fair distribution of money because there will always be a guy who will spend everything as soon as he gets it and the other one who will save and invest. Sooner or later one of them will be a millionaire and the other one will stay poor.
fair distribution upon creation of supply bud, not everyone has the same supply all the time.
every means of payment will sooner or later be monopolized (centralized) by some (smart,enterprising and brave) at the expense of others (timid, not as inteligent, etc.). You can't change that in any way, unless you create the future symilar to "Brave New World" by Aldous Huxley, where people do not have property but also desires, goals, ideas and any emotional deficiencies are drowned out by the perfect happiness-producing drug called "soma".
there is nothing wrong with bitcoin distribution. there is nothing wrong with the fact that in extreme cases, after a decade or two, a few identities will have 90% supply, because the future of the network is determined by miners and not owners (this is not a POS). There is nothing wrong with this as long as no one can steal or devalue money you already earned.