Did I not answer that one in Tyrion VI? Looks like I somewhat short-changed that plot point at the time.
Well, here goes. I think the main problem is ultimately one of timing: Tyrion’s got almost no men, and little in the way of food and other resources, that he can spare in the face of imminent attack.
And while I think a moving hand is certainly a novelty that the court will murmur about, I don’t think it’s quite enough to convince people to stop everything. Consider what happens when word reaches King’s Landing of Mormont’s death and Mance Rayder attacking the Wall – even though he believes the report, Tywin says it’s not his problem atm and proposes to do nothing.