Wealth inequality rises by default as rich people are able to invest more of their income than the average working person who is forced to spend a greater percentage of their income on consumption just to survive and live. This is simple maths and unavoidable.
In any society, there are always the rich and the poor. The Pareto principle says that 80% wealth belongs to 20% richest people. It is true in all countries and you can say it with their wealth in fiat currency, gold or in bitcoin.
The causes for this difference between the rich and the poor is not because of fiat currency or bitcoin. It is because the rich is more educative, more clever in manage their capital and can invest better than the poor. Knowing these facts, the poor can change their wealth by focus on education first, then invest their money wisely through which they can change their lives and individual, family financial status.
As rich people continue to re-invest the greater share of their income and regular people continue to be compelled to spend the greater share of their income on necessities, it won't take long until the vast majority of the 21 million coins are in the wallets of the very rich and once that happens there is no possible way to redistribute the wealth.
See
Bitcoin rich list. There are distributions of bitcoin and either you are Bitcoin whales or small fishes, you can accumulate more bitcoins. It depends on your thinking on Bitcoin, its future and your belief in potential of life change with Bitcoin investment.
If you believe in this asset, you can accumulate bitcoins with time. After some years, you will have good bitcoins in your portfolio that will change your individual financial status.