Will widespread BTC adoption exacerbate dynastic wealth?

Seems like it as early adopters get rich, and over time even if BTC sees wider adoption, the amount of existing currency will not increase beyond a certain point but the population as well as labor and productivity on average will increase. The world economy now is worth way more than in the past even when accounting for inflation because of this. On the one hand this is very useful because storing your money in btc will have it steadily increase in real world value even after the last bitcoin is mined, but on the other hand the already wealthy will pass their wealth down and become even more fantastically wealthy just from having btc as an asset. In the current economy this already happens because of investments though, no smart rich person just holds on to a bunch of liquid currency in a bank. My question is will BTC actually worsen dynastic wealth, or is it no worse than how stock market shares (specifically in index funds) do essentially the same thing?