> They will have one of the strongest incentive: to remain at the top.

At the top of what? After all the massacres the remaining billionaires and their families would be all that's left of humanity. Who would want to rule over a human-empty, machine-led Earth for the rest of their lives? Not to mention the attitude and morality of their families and those close to them.

I can think of several billionaires who would be quite fine ruling over a devastated and machine-led earth. Their families are chosen or bred to agree with their amorality, and they and their dynastic families would rule with pleasure.