An easy example would be something like flying PDX-SEA on AS, where there are flights every half hour or so (sometimes as close together as 15-20 minutes). You might have your flight cancelled and expect shorter lines airside, or there might be an earlier flight that you have time to make if you can get to the gate for that flight before boarding finishes. There's almost no question you're going to be able to be rebooked, so it's a matter of the fastest way to get where you're going.