"someone's been naughty and I'm all out of coal"

That's the joke.

The reason the joke is necessarily funny, is that we are supposed to assume Santa said it, since Santa typically brings coal to naughty children. But the image is not of Santa going down the chimney to hand deliver a coal substitute. His cheeks are squarely over the chimney hole, implying he has no intention of going down the hole himself, as Santa is no fool and knows the best way to avoid burning alive is by landing feet first. So what is he bringing instead of coal and how is it getting there? Well, again, Santa had his cheeks pressed against that smoke stack, ready to flick his trousers down and add a brownie next to the glass of milk.

I like your passionate defense of those passive sitters accused of being shitters though.