FWIW I pretty routinely board last and have literally never seen the door shut at T-15.
That's because Delta closes the door at T-10 (at the earliest) and not T-15. I've definitely seen T-10-ish minute door closures (which, ironically, always then seem to be followed by a 7-10 minute wait at the gate before the actual pushback). They say you need to be at the gate 15 minutes before departure, but they do not close the door until T-10 at the earliest unless all pax have boarded. And T-10 is rare, especially at hubs.