I'm not talking about real wealth inequality. I'm not even talking about fiat/Bitcoin distribution unevenness taken in isolation, without its effects on the utility of money (Bitcoin and fiat) as a means of payment vs its utility as a store of value. In fact, the former is of interest to me only as long as it affects the latter, since this influence determines the future (or fate) of Bitcoin and is the topic of this thread...
Fiat money, in this aspect, can be considered as a model, or a yardstick for gauging Bitcoin performance
You can think this way: If in future the transaction fee income raised to 50 bitcoins per block while the block reward almost decreased to zero, then every miner would become the early adopter: They can mine coin exactly like early CPU miners at 50 coins per block, and if they want to accumulate coins, after 4 years they would have 50% of the total coin supply
Technically, that goal is not unrealistic: Given average transaction size is about 0.5 bitcoin and a transaction fee of 0.005 bitcoin (1%) is acceptable, you only need to process 10000 such transaction in each block to reach 50 bitcoins, which is doable with 8MB blocks, quite manageable
However, in fiat money system this is impossible, the faster you make money, the faster the fiat money will be printed at magnitudes higher speed, so you always end up with a very small percentage of the total money supply
I don't quite understand how is that related to the issue in question. You mean to say that Bitcoin facilitates further accumulation of wealth (i.e. making wealth inequality steeper)? I'm inclined to think so (though for other reasons), but I don't see how this can possibly make it fare better (long term)...
Do you have any reasons how it could?