If I'm playing a Monk and a piece of Monk gear drops, I should have priority to get the item. Not because I deserve it more, not because I need it more, not even because I'm the one who wants it the most, but because it's psychologically satisfying that if Monk gear drops, the Monk has first dibs. This is basic game design 101.

Your proposed system would leave me at the mercy of the seal-hunting Paladin, the White Mage that wants the piece for glamour, and the Dragoon with the Monk at level 14 who wants to gear it someday. That's unacceptable.

"Oh, but you can just ask them at the start of the dungeon if you can have it"

Stop. It doesn't matter if I can ask them. It doesn't matter if I got matched with the nicest players on the server, or the biggest group of dicks who'll purposely roll just to make sure I don't get it. I'm playing the class that matches the gear that dropped. They're not. I get first dibs. They don't. Full stop.

Again, it's an extremely basic tenet tied to a non-stupid reward structure of any MMORPG.