Well, perhaps, even though nudity for animals is not considered shocking, perhaps he has a shirt on because again, he's anthropomorphic.
So why does he wear a towel on the lower half of his body when he gets out of the shower.
He has to dry off.
I always figured he wore a pair of underpants concealed under his feathers, so the towel would be logical... I guess... I mean, he would feel naked, right?