It's unlikely, I will ever play with this card, because I don't collect the novels, and when the character will be released in a deluxe expansion, they will give her some other weakness. But this looks like one of the mildest signature weaknesses to be released.
I guess, in most scenarios, if they carry Ancient Evils, you will stick them below. It's just so beneficial, to get these out of the reshuffle. If you hit your weakness, one of three AEs will re-enter the game. It will immediately strike for once, but chances are great, you still saved your group a few rounds with it, unless you draw your weakness really early. And the other two copies are save locked away anyway, unless you draw your weakness more than once a game, which I think, Gloria should not be a particular prone character to do so.
I think with other cards, like enemies or /-tests you are much better off with assigning them to the investigator best fitting the task, and scarce special effects like Daemonic Piping can be just discarded to hinder the set collecting of the game. Also, if the weakness strikes, it just opens a new slot for a new card. Maybe I would waste one slot early on, just to make sure, the weakness would not get shuffled back and creates multiple dead draws. But that's about the worst I could think of, this weakness might force you to do. Am I missing here something? Like I said, never actually played these cards.