Perhaps he should... or perhaps he did? Or.. perhaps you don't know what he did? Perhaps that wasn't the point?
People have different reactions to stressful situations - especially when not anticipated. My point was that i'd rather have the student fly the plane first before he thinks about to much else. In response to "Why then do people teach the 5 degree bank angle under these circumstances, as the rate of climb is less? ...and at this point, the climb is the point, I would think?", i'm merely saying that i hammer that 'positive bank angle' towards the good engine into my students so they don't forget to fly the plane. Saying 'don't worry about it, wings level is just as fine' might lead to some issues. That said, i only had one student that had these issues.