When structuring an argument for a game mechanic, try not to use phrases like 'it makes sense' or 'it doesn't make sense', since we are playing on a fictional continent in a fantasy world where not-radiation permeates through the world and wildly mutates people. Monk doesn't have to make sense when its surroundings don't from our perspective.
I would agree, though. Monk having no weapon marks seems out of character, but do remember that they also gain a separate progression table for their impressive unarmed strike table. I'm not opposed to the customary 3 levels in their favored weapon, since Monk is already a difficult start. A Monk that takes Brawler would be sitting on a +5 before stats, but Monk has a ton of penalties already in place that make me feel like this would be a minor change that would keep martial classes consistent with one another.