I actually really like this idea. Maybe having this on your sword would have drawbacks like maybe only giving the wither effect to mobs that are not undead. (zombies, skeletons, drowned, etc.)
I think this would be a nice idea. You could trade your armor slot to holster a backpack that could have not quite as much space as a chest, but maybe about 2/3 as much. It would also be cool if ...