... Would you do that with a sword that was likely more than what most people in old Japan would make in years (ignoring so-called kazu-uchi mono blades)?
I understand that different traditions do different things. But combine the status of the Japanese sword as one of the "three sacred treasures of Japan" along with the careless and senseless damage a mount and/or blade may take by being tossed away, ...
Well that where some of my thoughts when I experienced this etiquette for the first time.
When I asked the teacher of that dojo he told me that we talk about the sword of the enemy. It carries his spirit and should not be touched longer than necessary. And it would/should not be handled with the same respect like the own sword.
And I have to damit: I don't know how the sword of the enemy was treated in "old japan"?