Good question. In flight, we action the abnormal checklist as a read and do, solely by the PNF, with the PF confirming switch selections before they are moved. This is to ensure the PF (or at least somebody) is still "flying the aeroplane" at all times.
On the ground we do the same, but there is a good argument (as you suggest) for the FO (we don't have PF/PNF on the ground, only Capt/FO) reading the drill and the Captain doing the actions with the FO confirming, the obvious difference being that the aeroplane isn't flying anymore and cannot get into strife with it's brakes parked!
However, you would then have two different procedures for inflight and OTG. It's probably been deemed better to have one procedure of both. If I had my way, the Captain would be doing the reading, as that is where the stuffups/omissions will be, not the moving of the actual switches. He is purportedly the most experienced crewmember and therefore the least likely to mess up reading the "do" list.