So it wasn't a delayed flight, but it's kind of funny that just after I responded to this thread, something similar nearly happened to me.

My 9:00pm DFW-SGF flight last night (E175) had a published boarding time of 8:30pm (and a very light load). I was on the SkyTrain at 8:27pm when I got the push notification that boarding had started. I got off the SkyTrain at 8:29pm and started walking to the gate. At 8:31pm, I hear "This is the final boarding call [for my flight]. Once the door is closed, it will not be reopened." I begin running to the gate and round the corner at 8:32pm (28 minutes before departure) to see the agent tapping her badge on the reader and starting to close the door, so I yell, "I'm here! I'm here!" and sprint up to the podium. She stops closing the door and kind of rolls her eyes at me and says, "Calm down, let me reopen check-in."

While she's logging back in to her computer, four more people show up behind me who had apparently been at the restaurant two gates over and had seen me running.

Apparently I was literally two seconds away from the boarding door being closed (28 minutes before departure and 18 minutes before published door closure) and being left in DFW overnight. I know the rule is technically that you must present yourself at the gate 30 minutes prior to departure to avoid your seats being given away, but still...

Anyway, a reminder to not only not push it to the last minute if your flight is delayed but also not to assume you can always show up at the gate less than 30 minutes from published departure. (Will I learn this lesson? Probably not, but it's still a lesson. )