You have a point in saying making wealthy richer because they can able and easily do mining, investing, trading and gambling. But it's depends on the person on what the status of their life in accessing bitcoin.
Yes but who does all that mining, investing, trading and gambling? Maybe with the exception for the last activity, it is largely done by the wealthy of this world. Which proves the OP point, the resistribution will be very minor.
Crypto assets can run in two directions that you believe because they can run actively or passively, if we are active in short-term transactions, then wealth is the main goal, the opposite thing also happens for welfare where bitcoin always experiences a huge price increase and still in the path of initial fluctuations that will continue to develop.