"At some point" perhaps. But, aircraft are held at the gate for too many reasons to recount and that may sometimes run to an hour. I've been on several "last flights of the day" where we have encountered a hold at the gate at the last minute and where there is space and passengers have showed up 30-45 minutes late and been accommodated.

All it takes is a 2-hour ground stop due to weather in the Northeast and your "closed" flight may be sitting at the gate for a long time. Whether there is space, a GA will accommodate and Ops is willing to rerun weight & balance, is a different question.