To be clear- the only reason I brought that up was because the last person I mentioned the idea to insisted they'd insist the Bow was an Improvised Weapon and so even if a Monk took it as a Kensei Weapon you could not be Proficient in it or do anything else related to the idea.
We had an extended argument before someone else entirely pointed out we were dumb because mechanically you could just throw a punch and accomplish the same thing so hitting them with the Bow itself wouldn't be any real difference.
That's why I mentioned it. Mechanically there is no difference between using the Bow as a melee Monk Weapon and just kicking someone in the nads. Bludgeoning either way and the same hit die. I obviously want to use the Bow but if arguments arise I have the easy counter of the distinction between Bow and Fist being meaningless to a Monk.