AI doesn't have to be conscious or sentient to take over, all that needs to happen is for politicians, law enforcement, journalists, educators etc. to uncritically parrot everything it outputs. The military is already using AI to make targeting decisions. If they just go with whatever the AI says to strike, then AI is already fighting our wars.
The scary thing is that AI decision making has been infiltrating society for decades as an unseen entity.
As a bonus, mistakes can be blamed on AI.