At Midwest Express we run with the flying/non-flying method of work division.
I the case where something non-standard occurs the captain will ensure the
aircraft is being flown, but does not have to do so themselves. The captain
however is the only one that will call for an emergency checklist.
We have had a number of engine failures right after takeoff and just before
landing with he F/O flying and in all cases the captains elected to allow the
F/O to continue to fly rather then risk change of control that low to the
ground.
Jeff