Well, in a way it has, if you think about it this way. Using "take over" implies a fight for something. A revolutionary taking over the government from a dictator, etc.

However, AI doesn't need to conquer anything to "take over". Technology has already advanced so much that we are inextricably linked to it. Previous technology and especially computers have already taken over, and are integrated into every part of daily life. Some banks even require cellphones for two-factor authentication!

AI is the next logical step, and the world is already primed for AI.

So while AI has not "taken over" yet, we already have prepared a warm throne for it for it to chang every aspect of society.