Given a case like this I'd think that most people would delay their flight. The problem comes when you have connecting passengers or an inflexible slot. Waiting for a late passenger may mean that nobody goes anywhere or that people who have saved for months for a holiday miss their connection and have their holiday ruined. I'll run it to wire if I have to (leaving late, quick taxiing, flying fast etc.) but unless I'm told otherwise, I'll fly to make every connection.
PM