The underling mechanism for inequality growth need not include deliberate actions by wealthy individuals.
Wealth is generated based upon the work of accumulated capital rather than labor. Wealthy investors are making bets with peers that have similar levels of wealth. Since neither side is actually creating wealth from raw goods, on average there are equal numbers of winners and losers.
There are good arguments that too much inequality is detrimental to social well-being. Without deliberate mechanisms to redistribute wealth downward, inequality will grow without bounds out of statistical necessity.
Managing inequality means introducing mechanisms that redistribute wealth more equitably which are at least as strong as the statistical effects which naturally concentrate wealth.
This is where greed comes in !
In practice, those that have attained wealth, even if by the throw of the dice, feel entitled to their fortune and resist any attempt at leveling the playing field.
Whether it is luck or skill that is involved in negotiating one’s bets, winners consistently attribute their success to skill, and with that comes a sense of entitlement to their winnings.