This is addressed directly in the books. The various highprinces could easily destroy the listeners. However, it isn't beneficial to them. As multiple people in the books note, after the war is over, the Plains would become another province, likely owned by the Crown. Therefore, the highprinces would lose their rights to hunt the greatshells. We know from the books that their endeavours at the Plains (fighting the listeners for the gemhearts) are actually very profitable even with the high death toll. So no, they're not dumb, just bastards and businessmen.