As you know from the quest text, all the crafting writs are to make supplies for the Alliance War. That is how all the guards get their supplies.
Since we are finally introducing a faction lock to stop the cheaters and spies, we need only allow a player to turn in writs for their account-locked faction.
Otherwise, they are aiding and abetting the enemy cross-faction and it's just not fair. It breaks my immersion entirely to fight guards wearing armor someone in my faction made on a different faction character.