Or would the distribution be even more unfair?
For some reason, it will still a little bit unfair. Wealthy people do have an edge because they can buy many bitcoin right before hand. Unlike other people who have bitcoin just because they do some things in exchange for their service. But as to opportunities to earn, it is given to all equally.
I think wealth is not distributed evenly because many of us are not connected with bitcoin and with it they will not feel the benefits. Many bitcoin users are now rich. And wealth is in the hands of people who are eagerly working hard to make more money