For this analogy to fit, the bank robbers would have to destroy (some of) the notes/coins/gold bars (that is, the stuff both parties care about), not execute people (whom the robbers don't care about but the other side do). Which would convince the other side not that the robbers are serious, but that they're idiots.

Well, if you don't have hostages, demonstrating that you're capable of destroying the entire bank vault if they don't let you walk out with half makes sense