I did exactly this the last time I went to Department of Transport (WA). I was still 36th in the queue 20 minutes before opening. I think I had a whinge about it at the time.
I definitely had a whinge about the first attempt, when I was turned away an hour before closing because they weren't going to get through the people already in the waiting room.
All I was doing was collecting a number plate. 2 minute thing.