That isn't what I am saying at all. What I am saying is that, you shouldn't be able to use a feat that is intended to be used during your turn if it isn't your turn! You can't cast a spell as an AoO. You can't drink a potion. You shouldn't be able to draw a weapon on an AoO - even with quickdraw - or loose a shield. You can't take a 5' adjustment during an AoO. These are all combat related actions, all requiring that same skill in combat that is also represented by BAB - and feats. Why, then, should cleave be different?
Normal attacks/round are due to you pressing the attack - as you get better, you learn to press the attack harder, and get more opportunities to actually score on them - thus, you get more attacks/round.
IMO, an Attack of Opportunity isn't a full-on combat attack - it shouldn't follow those rules. It is a small opening in someone's defenses, and you stick your sword through it as they pass by. They are created by the target, not the attacker - YOU do something stupid and let your guard down, and then I smack you in the face for it.
Basically, I realize that the rules don't prohibit it from occuring. But I don't think it should.