If the check-in deadline is 15 minutes for domestic flights, then I think it's reasonable if they close the doors at 14 minutes prior to departure, even if not all ticketed passengers are checked in. There are probably many ticketed passengers that no-show for every flight, so waiting just because there's a ticketed passenger that's not checked in would mean waiting for essentially every flight.

Some people may argue that flights should never leave early. My opinion is that it's okay, as long as it's past the official check-in deadline. Passengers arriving at the gate after that time run the risk of missing the flight for any number of reasons: overbooking, weight restrictions, or in this case early departure. I think that there will be many passengers on each flight that would benefit from arriving early at their destination.

But in your case, if you were at the gate 21 minutes prior to departure, and they had already closed it, it would seem to me that you would be entitled to involutary denied boarding compensation / accomodation.