People take all kinds of trophies. Some of them hang stuffed animal heads on their walls, some have a collection of left hands.

[ Amongst other things. Presenting one's lord with an enemy's head was considered a great gift too, in certain cultures. Not that Kojirou ever did any of that. He has little interest in trophies for the sake of trophies. ]

Perhaps more useful is not the head but what's in its mouth. A dragon's tooth can be intensely magical. In fact, all parts of dragons are rather useful. Do you think we could get a cart to take it back home with?

[ Dragon steak for everyone! ... Maybe. ]