Staff seem to like that. When waiting for my train at vauxhall, I often see guards start closing doors before everyone has made it on. I know there is a delay becaise of the warning tonebut vauxhall has quite a mighty gap so it's really not a good idea to rush people like that.
As for terminals, if it was an elderly person, for example, who was rushing after being notified of the platform at last minute, would they wait if she was already near and the signal to close the doors was just about to be given but hadn't quite been just yet? Say this is an intercity train so even once the doors are locked, it wouldn't move for another minute.