The government is made up of human beings too. I doubt most of them are psycho to such a degree as to let 99% of humanity die for no real reason.
Game theory is a helluva thing.
And I do not have much faith in the charity of the most powerful 1%. Charitable people often do not make it into that group.
They will have one of the strongest incentive: to remain at the top. Moreover, it will not be that hard. In Soviet Union one honest socialist with four revolvers (major general Vasily Blokhin) could easily kill up to a thousand people per day personally (if he were laboriously working overtime). And back then there wasn't even a global governmental surveillance or AI-drones with explosives.
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.