The distribution of bitcoins is pretty bad, but I have no idea how it is evolving. There are many processes going on, some concentrate the coins (for instance, "professional" robot-driving traders collecting coins from many small traders) and others distribute them (for instance, large holders cashing profits by selling at exchanges, directly or through Bitpay). Who knows which kind predominates.
Fiat tends to have poor distribution as well. I've wondered if politics allows newly created money to be concentrated to a few at a faster pace than can trickle down to everyone else. They never see the "trickle down effect". With bitcoin, eventually the new coins stop and has no choice but to slowly become more distributed.
There are at least a couple of threads discussing the distribution of coins by owner:
Those analyses suggest that the distribution of bitcoins is a bit more unequal than the distribution of wealth in the world.