For instance, bad pathfinding in an RTS game can make the game almost unplayable. Halo is just about legendary at this point for teammate AI that is worse than worthless . Any one of these things can destroy immersion at a critical point.
AI is to video games as IT is to a modern enterprise. If it's doing its job, nobody notices, but if it's bad, it sticks out like a sore thumb.
My former company had a backgammon game with a really good AI. We constantly got accused of cheating, even though the dice-roll algorithm was identical (it didn't have a parameter to specify who the roll was for). What people missed is that a good backgammon player will position themselves to benefit from a wider set of possible dice outcomes.
This is what I said though. A game's failures can be blamed on bad AI. But once you reach the point of okay AI, you stop hearing about it. There's very little reason to put in whatever effort is required to make your AI great, because the only people who will take notice are hardcore players who put in tons of hours. And that's nice and all, but the game costs $60 whether you play it for 10 hours or 100. So why spend millions on a feature that's hard to make a trailer for, and is only noticeable to your most hardcore fans?