This is a bit too "spherical cow in a vacuum" for my tastes. As a quick experiment, I included population growth (using average population growth rate of the US over the last 50 years) and GDP growth (again using US average for last 50 years). Assumptions being that new population start with $0 and GDP growth applies equally to all as a percentage of their then-current wealth. It substantially enhanced the inequality.

In the simple run, median/mean was 67%, but with compounded growth it was only 7.9%. Moreover, the standard deviation went from 1.31 times the median (87% of the mean) to 17.83 times the median (141% of the mean).

https://gist.github.com/anonymous/4f6c546a776a8ab142235c8617...

Wonder what it would be like taken further - forcing population that have $0 to take a loan from the wealthiest people and pay them interest.