Not even. Humanity would consist of a small elite who owns everything, a small, continually shrinking middle class that consists of the remaining few workers who are actually needed for some reason (eventually, this tiny middle class would shrink to just the members of boards of directors, or something -- someone has to supervise the machines even if it's just rubber stamping them) and a vast underclass experiencing a life similar to an urban homeless today or a hunter gathering tribe in the amazon or something, existing in the margins, trying to steal, beg, scam a bit here and there to survive another day in whatever weird insect-like social niches are left to be found, that are just too marginal for the elite to even care about, even with their optimal AI.
Look at life in Gaza or on the streets of Kensington today, and that is the sort of destiny we are bound for -- if fully replacing all humans really ever happens -- to become totally disposable people, who only continue to survive because someone has found it too much hassle to get around to getting rid of you at least just yet.
But that's an endgame state, it's not a path for getting there, thank goodness. I believe it would not be so simple. It would happen gradually, and it would engender resistance, eventually violent resistance once people have little to lose.
Power grows out of the barrel of a gun after all.
Now, OTOH, if at that point, robot/AI weapons are sufficient so you only need 10 people to run the entire US Army.... then it's game over.
But can you even get to that state without provoking a war before you get there? AI is extremely vulnerable in war because of its reliance on datacenters and fabs, which are fantastic military targets in wartime. So easy and quick to sabotage and so expensive and slow to build.