Actually that's a rule of comedy. Three times is the golden number for a funny bit.
It's funny you should say that, because I've had and read quite a bit of discussion on that. There is a principle that if you repeat something three times it becomes funny
but always when the third time is with a twist. So for instance, you put a bucket of water on top of an open door, I walk in, it falls on my head. Second time, bucket hits me on the head again. Third time, I open the door without entering, no bucket, I walk in confidently and step on a rake that smacks me in the face. That's basic physical comedy.
The problem with the carrot as a comedy bit is that it was essentially the same thing each time. Carrot in the eye, carrot in the mouth, carrot in the gun. For it to be comedic, it would have had to be (1) impales the guy with the carrot; (2) impales another guy with a carrot; (3)
tries to impale the guy with the carrot but instead the guy eats the carrot so he just shoots him. Of course comedy theory is bullshit, you either find something funny or you don't and then you find reasons to explain your reaction. Sort of like music.
I've heard of another theory called the "Rule of 3 and 7", that when something is strictly repeated, it's funny for the first three times, and then again as of the seventh repetition. Family Guy does this a lot. After seven repetitions, you've entered a sort of metahumor region where you're thinking "there's no way they can possibly keep doing this" and they defy your expectations. But I don't really find this funny, personally
