Hah, no. They get rich, because the more wealth you have, the easier it is to increase it. Why? Because this is how the rich and powerful have set up the rules of the game.
Personal wealth does not correlate with any sort of "value" you have personally created.
> They get rich, because the more wealth you have, the easier it is to increase it.
The more wealth you have the easier it is to provide value to other people. That's known as capital investment, and it's how wealth begets more wealth.
Or they could just spend all that wealth they've saved on themselves. People inclined to do that generally don't become wealthy in the first place, however, barring abnormal circumstances such as winning the lottery. A habit of frivolous, conspicuous consumption is a good way to ensure that you don't stay wealthy for long.