I don't see any need to complicate it by making the recipient dirty themself. The punishment I've always known is just about
(a) the pain of the insertion and the reinforcement of the idea that someone "in authority" can open up your dirt-hole if they see fit; and
(b) the evacuation of the excrement, retention of which caused the autointoxication which caused the errant behavior in the first place.
And as I learned the hard way, when you have a persistently constipated child and they're over your lap for a spanking, it makes sense to kill two birds with one stone and put a soap-stick or jelly bullet in while they're there. To paraphrase my mother: It's "punishment" to the child, but it's medicine to help them do a smell - can't be bad, can it?