Many human traits and attributes aren't self-reinforcing. You don't get taller by being tall. Having red hair doesn't make your hair redder over time. Even across generations, regression to the mean causes the children of extraordinary individuals to be less extraordinary.
Intelligence and ability at sports can be mildly self-reinforcing. Being told you're smart and encouraged to be smart will lead to a positive feedback cycle of confidence and success. Being told you're not smart can also be a self-fulfilling prophecy. "Stereotype threat" can come into play; even being reminded that "people like you are not good at X" can make students worse at X.
Hockey players in the junior leagues are disproportionately born in certain times of year. Their extra age and growth when they start playing hockey serves as positive reinforcement. It might not matter at the very top of performance (see https://www.bloodyelbow.com/2012/1/4/2681038/out-liar-what-malcolm-gladwell-gets-wrong-about-the-relative-age; the "relative age" effect disappears in the NHL.)
But even ignoring factors like that, a top professional athlete is way off the bell curve on performance. Not because they were born that way, but because they trained to be that way, and any initial advantage has been reinforced by sustained effort.
Wealth is extremely self-reinforcing. Even if natural ability to earn money follows a Gaussian distribution, it's much easier to earn money when you have money than when you do not. Wealth isn't subject to regression to the mean; even heirs who spend all their inheritance can remain wealthy for a very long time.
At high levels of wealth, it's not the earning power of the wealthy individual that matters any more. It's the ability of the advisors and managers who are taking care of the wealth that determines how much it grows. Wealth generation can be outsourced in a way that other human capabilities cannot.
That's a really good question! I'd say that it has to have a lot to do with network effects. The extremely wealthy have political influence at a national or international level the lower upper class with their local influence let alone the middle class can only dream of.
With the concentrated ownership of the business sector, you will often see startups that are forming into viable competition either bought up or crushed. In countries like Japan, there are large conglomerates called keiretsus that own entire value chains from mining to all levels of industrial production and logistics to retail and even finance. By controlling entire value chains such large conglomerates are able to keep competitors at bay and wield enough political power to make sure the rules stay favourable to them. It is said that power structures of Japanese society bear great resemblance to feudalism to this day. Between half a dozen and dozen keiretsus dominate the Japanese business sector to date. They include familiar names such as Mitsubishi, Mitsui, Sumitomo, and Toyota Group.