I'm at least 50% convinced that there is a natural selection where managers are the people who like that stuff but people who stay developers hate it. I totally agree with you, from the moment I step into one of these rooms with my laptop in hand I just want to get out of there and back to my chair, my monitors and time to think things through.
1) creative brainstorming (ux, ui, branding, early architectural decisions) to ensure everyone can present and validate their ideas, and people are more on board with decisions as they saw democratic backing (or, at the very least, feel that objections they raise were heard!)
2) bringing staff that would normally be spread across multiple buildings and units together - the bigger the org and the more stakeholders involved, the more important a common space for (at least) the leadership team is, especially to cut through red tape and organizational barriers.
3) when you have an immediate problem (outages, GDPR incidents) to solve and secrecy is involved - no need to take care about people not in the loop, seeing stuff they are not supposed to etc.
What "war rooms" often enough end at, unfortunately, is cramped chicken coops. Not enough space, sales/PM people directly sitting and blathering in their phones next to developers, ... for months. That's a farce.
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.
