I've been "that family of 6" that shows up at the last minute. Every time, we were listed days ahead of time on a different flight that ended up looking bad, and we chose a different flight/route to get where we wanted to go. Here's my example from this summer:

Planning on going to Paris from a hub city. Flights were bad, bad a week ahead and didn't get any better, so we planned on going Hub-London-(ZED fare)-Paris. ON THE WAY to the airport, I casually check the direct Paris flight and see its now got 25 open seats. Well shoot - lets do that. So when we pull in the parking lot, we switch to Paris and go check-in. Turns out a DFW-hub flight was 3 hours late for thunderstorms down there and a large group was going to misconnect. We got on and avoids the hassle of going through London.