People leave empty handed all the time. I've tried to pick up a package from the depot near me twice, queued for ages and not once been able to actually collect my package. I've had to arrange for my flat mate who get's friday off work to pick it up for me on a quiet day.

I'd say the right way to do it would be to have full day opening hours on a saturday. The variable length of the queue on different days provides some great insight that's currently being ignored.