But if, say, you are traveling with a pet that has to be verified at the counter, or you need to check a bag, the time windows for accepting those are set by the scheduled departure time. If your plane is still in the air or hasn't even left its origination airport (and, for the sake of argument here, we will assume you are flying from a smaller airport that doesn't have other aircraft that can easily be reassigned to your flight, so you know it will be delayed), it doesn't matter: they still close the check-in and baggage 45 minutes (on American; YMMV by airline) before scheduled departure. So you have no choice but to get there early and wait unless your airline actually declares the flight delayed when they know it will happen.