I wonder how often, if PF is selecting reverse, the reverse selection is "fumbled" because the PF "misses" the reverser levers because he is (hopefully) looking out the window.
Also on a type (like wot I fly), where reverse is available and normally used on all four engines, and, say, one reverser doesn't unlock, that certainly would be less of a distraction to the PF if the the PM is selecting reverse.
In my airline PM selects reverse.