Here's an interesting demo on how wealth tends to redistribute toward inequality.
This Interactive Demo Illustrates A Simple Truth That Influences Income Inequality
To run the demo go to the prof's site:
https://en.yaronshemesh.com/inequality/.
The answer is no. In time the money will be redistributed toward increasing ineaquality:
More interactively:
https://lucasvw.github.io/assets/videos/money.mp4
The math is here:
https://lucasvw.github.io/main/2017/06/22/money.html
This is what happens naturally. The government may interfere and redistribute toward equality but in the long run inequality returns.
Nozik, a political philosopher, explained this with the Wilt Chamberlain argument. Say you have a society and you distribute wealth however you like, let's way according Rawls's Difference Principle so at the start everyone has the same amount. But in this society live Wilt Chamberlain, an extraordinary basketball player that people want and choose to pay to see. In the long run, once again, you will end up with a distribution of wealth that tends more and more toward inequality.
And, as Nozik contends, since it is voluntary, it is not only natural but moral.