As a pilot: The issue BALPA has is a very valid concern. The suggested procedure having both pilots involved goes against all training, you want clear split dut

As a pilot: The issue BALPA has is a very valid concern. The suggested procedure having both pilots involved goes against all training, you want clear split duties in an emergency where one pilot flies the aircraft and the other handles the checklists (you could call it "debugging") for the problem. There have historically been avoidable accidents where two pilots lost the big picture because both were involved in dealing with a problem. That resulted in the current structure of crew resource management (CRM) being designed to have one pilot flying the aircraft and the other dealing with a problem. In many cases if the captain is the pilot flying the aircraft and there is a major problem one of the first steps is to hand control to the first officer. Contrary to some beliefs the copilot is at least as qualified to fly the aircraft, and this allows the captain to zoom-out and make a decision on what to do next such as diverting the flight to a nearer airport. If you design an emergency procedure that requires both pilots just to control the aircraft, you'll loose a huge part of the decision making and planning abilities of the crew.