With fiat, the ruling wealthy can continuously inflate the currency and still maintain their wealth without redistribution.
Speaking as a Bitcoiner,
1. Bitcoin is a deflationary currency.
2. There is no guarantee it "will eventually be irrevocably distributed."
There is, assuming bitcoin is used as the one and only currency.
If you want food, you'll need to pay with bitcoin.
If you never do anything to earn bitcoin, you'll just keep losing bitcoin to pay for food. Thus, unless you were incredibly rich to start with, you'll need some form of income (= you need to offer something to mankind) to pay your food. You can't just print your way out of it like the rich do now.
Yes, early investors will likely have enough bitcoin to feed themselves and several generations of children and grandchildren but eventually there will be a somewhat even distribution. Since the few people who are rich enough in bitcoin that they don't need to work will only lose bitcoin (they will spend more than they earn), while the relatively poor will work and earn more than they spend. Eventually the gap between poor and rich will close.
That's the effect of a currency that is limited in supply, like gold or bitcoin. At some point, you will need to do someone a favor to gain some commodity in order to get something you want.
There are no free rides in a commodity-based system.
The gap between rich and poor is caused by a lot of things, unlimited printing of dollars is one of the causes (not the only cause however).
Another important cause is because a majority of people is stupid enough to refer to other people as their 'boss' like they are some kind of dog.