Why does it seem like my wife prefers to rush our son out the door when she comes to pick him up?
She may be trying to keep it short so she won't have to engage in a conversation or something. I'm sure she must feel uncomfortable as a result of her decision making.
Does your son cry to stay with you? If he is showing signs of not wanting to leave, then that could be her reason of not prolonging the exit scene.
We could guess all day. It's another one of those hard things to see your family (your son) split like this.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!