As a cynical take: Often the real purpose of a war room is not to actually solve the problem, but to provide visible evidence of Serious Business™ Happening, even if it's all just performative. A product owner calls a war room to visually show higher-ups that things are happening and people are nebulously doing things and looking very serious while doing them. It's performance art, but it is re-assuring to the people paying the salaries.