But if the plaque is essentially tagged as treasure, is that any different from tagging something as a quest item? Why wouldn't the player carry it with him?
Yeah. As I said, this is slightly contradictory.
I'd rather players think "hmmm, this must be important.. I wonder what for...", then read the text and solve the puzzle. Keep in mind that this particular quest is a secret one - it won't appear in the journal.
It's an alternate ending purely for story telling. The game can be finished without it.
Some players won't WANT to carry it, mainly as its weighs as much as 5 "average" items.
As for overt quests, ie "collect 10 pig ears"; whilst I'll not do them myself, the quest engine will allow it. Even for these quests I'd rather the player read the quest journal and remember what it is they are supposed to collect.
I'd dislike marking something as a quest item if the player hasn't started that quest. "Oh! A nice red, mundane item! I'd better collect 5 of them.. not sure why! Hopefully someone will ask for them in the future!".