Investing that money, or otherwise allocating that money to companies who can better use it provides value to society at large, and in return, the person investing will receive a return on investment to live off.
To point to someone who has done the research, 'Capital in the Twenty-First Century', states that its not a self-correcting problem. Furthermore, I'd argue that index investing make it incredibly difficult for his heirs to lose their money. Anything short of a collapse American global hegemonic power means their wealth will be relatively safe. Furthermore, investing is not means of wealth redistribution. I can invest billions in Wal-Mart, but that will not motivate them to pay their cashiers a cent more. The compounding effect of the wealthy owning most of the industry through the stock market means their share of the ownership grows, leading to headlines like we see.
https://en.wikipedia.org/wiki/Capital_in_the_Twenty-First_Ce...
You can build a dynasty around land because ownership is barely taxed. Land does not degrade by simply keeping it vacant. Meanwhile everyone around the land needs it to live on or to work or to extract resources. Inequality isn't driven by well deserved high returns, it is driven by monopolistic extortion where you cannot refuse even if you know you're getting ripped off.
I addressed this in another reply, but I find it funny that you questioned that point literally after showing an example of it to be the case. Clooney leveraged capital from acting to buy a tequila "factory" (AFAICT, he didn't run the company, he didn't make tequila, he didn't manage distribution, his name was just on it), and used that capital to make more money they he would have ever had from acting. But somehow #2 is controversial on HN.
1. George Clooney didn't get rich from acting. He got rich from selling Tequila. Regardless, his children will likely remain wealthy despite never having been on a movie screen, much like the Waltons are among the top 20 richest people despite never having a job at Walmart.
2. Every year, fewer and fewer people get rich from having built something (labor), and more are just rich from being already rich (capital).
If in a free-market system, if you let the people with most wealth concentrate power, after n-years you are just left with a monarchy with a couple extra steps.