Sounds like you're describing some impossible system but that is how it works in the rest of the world. There's a time at which the gates close, and if you're at the gate before then then you can go on the flight. If not then they might wait for you for a bit if you've already checked in but nothing is guaranteed.

They can still go early if all of the passengers have boarded.

I got to Dublin airport once at the time that the gates were supposed to close and they said they would wait for us if we were fast... Got to the concourse and it was the furthest gate possible - the sign said to allow a 15 minute walk! Had to run all the way but we made it.