Flaps One is exactly right. Let us imagine the situation. 757 at Heathrow Terminal 1. 170 passengers on board, going to, say Frankfurt on a morning service. Lots of businessmen and women with important meetings to go to, big money riding on them.
Captain makes an announcement along the lines of this:
"Ladies and Gentlemen, we originally had a 40 minute ATC Eurocontrol delay. I was offered a slot in 5 minutes from now but I have turned it down to allow Mr Smith to make the flight, who just phoned us to say he is stuck in traffic on the Heathrow spur, and should be here in around 25 minutes."
Aircraft arrives in Frankfurt 25 minutes late. Many passengers miss their meetings, lose their contract. Not just this flight but all flights operated by that aircraft for the rest of the day. All these passengers claim compensation from airline for delay. Said airline would be bust in no time.
Get to check in on time, thousands manage it each day.