If she survived his attempt to permanently silence her that would be incredibly satisfying. Everything he does to try to extricate himself involves doing worse and worse things and digging his hole deeper; it's like he got all Dark Coop's evil genes but none of his competence ones.

I'm gonna go with the latter. Plus, chickens are funny birds.

The joke is that the answer is not the twist answer you expect in a joke, but obvious and literal. It can only exist as the classic joke because it was composed after the conventions of jokes were well established. It's a wee bit paradoxical.