You're missing my point: The point where they stop chasing money, or power, or anything you want to call it, is when they have it ALL. They are not a homogeneous group. More than one want everything, and they will burn the world down to get it. The point where stopping is even forethought will be when the guillotines are at the door or humanity is wiped out.
One problem with your ending: They can't stop taking, so they won't stop short of where people will riot. The rich will never reach such an equilibrium state because one of those psychopaths has to be the emperor and others will always try and usurp the power.
There is a private equity firm for every industry. Daycares, physios, dentists, everyone. They all make them "efficient" by cutting services and maximizing profits at the expense of the public, and there's seemingly no way to stop them.
The AI from the movie I, Robot. The one that Will Smith destroys. The one that wanted to protect everyone from ourselves.