One more thing I noticed while testing, as a farewell present:

Necromancer Staff is supposed to give 10% Magic damage.
But Gaze of Nagash, which according to the combat log, does Magic damage, doesn't change its damage.
Staff in Inventory, Staff in Loadout, Staff equipped (as in: I will swing it when I attack), Staff not equipped all say 100% and do the exact same damage.

The Necromancer clothing gear, on the other hand, seems to work fine. With 4 pieces equipped, the combat log states 140% and the damage number is higher.

I suspect the damage multiplier would only work if the Staff would be equipped while casting. Since if having it in the loadout would suffice, one could just put 4 Staves in the 4 weapon slots for 40% increased damage.
But since a cast automatically unequips the weapon and the player is therefore unarmed while casting, the bonus does not work at all.

This is obviously just a suspicion, since I have no access to the actual code. I just guess that's how it's done and that's what's happening.