Turning off that AI logging stuff might be a terrible idea if that's what the AI uses to make future decisions. You'd be making the stupid AI even stupider.
And no, the AI doesn't move its units one by one, it moves them all simultaneously. Calculating the AI's decisions and updating the game state is what takes time. It's likely not very well optimized. Keep in mind that if Firaxis listens to all the complaints and improves the AI, turn times will likely only get longer.