A colleague points me in the direction of research that large brainstorms can be fruitless. Highlights from the original research (in her summary):

“There is considerable evidence that group brainstorming is less productive than individual brainstorming”. Explanations for this “productivity deficit” include “social matching… a tendency to conform to peers” and “social loafing… because responsibility is diffused”. The researchers focus on a third , viz “collaborative fixation” — “Exchanging ideas in a group reduced the number of domains of ideas that were explored by participants. Additionally, ideas given by brainstormers conformed to ideas suggested by other participants.”

As she mentions, the experiments were conducted using computer terminals (presumably to enable the researchers to control the environment) and so it’s not clear how face-to-face interreaction would have affected the result.

So what should you do if you find yourself in a timesuck meeting like this? Doodle.