I would tell parents they need to have someone (doesn't have to be the parent) pick their child up within 30 minutes. Period.
My daughter came very quickly.
My sister gave birth within a hour for all three of her children. The doctors all say she was "made for making babies".
It's best that you are as prepared as possible (having a back up person come in the event a parent is late picking up) and the parents are prepared as possible (have back ups to pick up children in the event they cannot get there on time).