It may be they're worried about it getting stolen. Especially during the festival, where it is much easier for a mage to sneak in. Aleister told Archbishop Laura Stuart that the defenses were reduced because of it.
What makes it a problem is the very nature of the stab sword. If it gets stolen instead of traded, then you have a weapon capable of killing any Saint with just a poke, only now no one involved knows who has it. As they put it, Saints are used for deterrence, like nuclear warheads. They'd be losing a device that can neutralize all of country's nuclear bombs.
If it is a legitimate trade, I wonder if boobies mage thinks Touma is trying to steal it. There is fishy stuff going on here. Laura Stuart is a liar and a supreme manipulator. Who knows how much truth she is really ever saying.