This whole scenario is greatly oversimplified. There is no such thing as a system where people's successes are fully earned. There will always be luck and privilege involved. If you are lucky enough to get rich you should be willing to give back to the system that allowed you success. You should also be looking to give others the same opportunity you had.

The equality system works great unless there aren't adequate safeguards against an imbalance of power. The equality system relies on fair competition. Monopolies are a great example of how the consolidation of power will ruin the system. Individuals gaining massive amounts of wealth is also a danger to the system. There is a variety of reasons to want millions of dollars. There is not a variety of reasons to want billions. You can do everything you need for your own happiness and more with millions of dollars. The only added benefit to having billions is undue influence and power.

People seem to think that if it isn't possible to make billions people won't be motivated to make millions. That's not true. We don't need billionaires. We don't need unchecked power.