I think we all know exactly the type you're talking about. They've usually got importance keys clipped to their belt and an importance 2 way radio in their hands.
When I'm up against them I take great pleasure from the fact that they behave that way because their husband is almost definitely nailing his secretary. She can't afford to leave him because she can't afford the lawyers to fight for custody of their fat kids.
Actually not really, she let them on the flight despite the fact the check in was passed the cut off, they wouldn't have had an issue if they didn't turn up so late.
As for the moaning about how she wouldn't let their baggage on despite it only being 100ft away with minutes to go. Luggage just doesn't get tossed one by one into the back of the plane. If they have a timeline of things to be done, and they say the last baggage crate has to be loaded on the plane at X time, and the baggage is on the plane, you can't easily just go and add another one. There are checks to be done after everythings on board, they are locked down tight, tied in, doors are properly shut, nothings left open etc, etc.
If theres a time and they missed it, they should just delay everyone that was there on time for people who got their late?
As for the plane still being their twenty minutes later, doesn't make the blindest bit of difference, at all. They closed boarding and shut the door ready for takeoff, if something else happened, an extra check needed to be made, thats life, the doors are still shut and final checks being made. You can't just leave the doors open and let anyone on at any time.
There are many airport stories full of woe and anger, yours is not one of them. Yours could be summed up in one line " I was late, it cost me my flight, this other couple were late also, they missed it".
Flights canceled, bum probing looking for coke, a bomb scare, overbooking and getting screwed out of your seat, delayed flights sitting waiting for hours or days, etc, all things to complain about, some fairly, some are just due to life and unavoidable, your's doesn't rank anywhere in list of terrible customer service stories.
I've never had an issue with flights, the biggest issue, and slightly worrying, was my first flight after 9/11(though it was like 2007

) was too New York, and just as we were due to leave, the plane was stormed by armed guards looking for a criminal, who they lost track of in the airport and determined wasn't on the plane.
I would also say while I normally wouldn't, I know my loud mouthed mother(in a complaining about anything, not a chavy way) would have probably asked someone, after waiting for ages with the flight approaching, if they can make sure the plane crew, the gate crew, and the security guys know that everyone there was going for the one plane. Could they open up the second security gate now and make sure everyone got through, can they make 100% certain that the plane crew knew they were there and checked in, just a security hold up. They might have happily held the plane, with advanced notice, or done everything to speed it all up. But if they last customers appear to have arrived and its time to go, and they lock everything up at that point its a big ask for them to change everything around. Even I would have asked someone about the situation and seen if they could do something about it BEFORE it was too late, not after. Then again, I would have been there with an extra half hour to spare, and a book.