Well it wouldn't necessarily need to be everyone babysitting an artifact, but some characters might. With any of the proposed stuff, it will suit some but not others - not all magic can help other departments, not all magic is offensive and has combat uses, and not everyone can teach their magic to someone else.

Really, a daily task would just give people something to make an open post if they wanted to. Some good posts for medical have just been of them hanging around in the med bay doing day to day things.