It’s kind of like the “who sets the stab trim” thing. Just like they are preaching now about reviewing every page of PWB before the captain sends it to load (it’s part of this year’s recurrent talking points). It just slows down the flow completely when we are about to review it on the checklist anyway.
I also as an FO usually do the book and send the post flight. It just works. And I also appreciate the quick bail at the end of a trip.