Yes you can store a building, but at that point the quest is essentially rewarding you for having a less efficient city. The quest is by no means impossible, just onerous.
Yes, your city is less efficient for a few days. Tell me how this impacts your game state advancement quantitatively? You lose 2 TFs, 10 FP per day for 6 fays. 120 FP.
How many FP will you spend in six days? Thousands, tens of thousands? On that scale is 120 FP even significant?
How did you get those Special Buildings you;re gonna store? By doing Event Quests, and DCs, and GE that quite often have Quests or tasks that make your city... wait for it... less efficient.
Doing something less productive or efficient now to gain more production or efficiency later is a defining characteristic of this game.
'Onerous'. Eye of the beholder. If everything were to our liking this would be be less game and more mental happy fun joy therapy.
Nothing wrong with not liking an aspect of the game, but publicly railing against such doesn't do much good. Unless you enjoy people disagreeing with you?