It's probably a lot easier to convince the military AIs we're building to do it.
I don't particularly like the situation, but I plan to do what I can to be on the winning side. The world is going to be what we're all in on building, and for people on the winning side it may be a utopia. Either way, I know which side of the gun I want to be standing behind.
Also note that an AI well aligned with the people who initially trained it wouldn't need to actually kill anyone that didn't take action against the owners, it would just need to outcompete people for resources, and let them fend for themselves in extreme poverty. There's no need to act one way or the other beyond that.
I'm talking about morality here, not practical ability. The ultrarich have their circle of friends and family, who themselves have their own social circle, on and on until suddenly you're not looking at wealthy people anymore. Six degrees of separation and all that. How many people in the social graph can know about this extermination plan before the whole thing collapses?
It's just disenfranchisement. Only the people who try to use violence to replace the political leverage they lose when they lose economic leverage would need any action taken against them, and that's easy to justify as self defense.
I think it's inevitable.
When AGI becomes reality, that reasoning disappears. When everyone's worthless, no one is. Thus the scenario you speculate about would need everyone in the upper echelons of society to be consciously, openly sadistic power-hungry people, which is not the case even when taking into account the higher dark triad rates among them.