There should be a function for automatically closing the boarding desk. Maybe even adjust between “close at exact time”, “close 10 min later” etc.
Then the problem with a passenger always coming late and delaying the plane will be gone.
My planes almost everytime leave late (some can stay for hours, even a whole day) after the plane should have left because of one or two passenger that don’t find the boarding gate for some reason.
When boarding closes 16.30 it should close 16.30 (or delay f.ex.10 min if you want), so the plane can leave (and the late passenger must go home).
In real world they don’t wait forever