The commander handed over control... Good call. Flying, analyzing, communicating, decision making, all together is not easy.
I would dispute this. Handing control over to the FO is good, but only
after the pair of you have placed the aircraft into a nice stable condition. Monitoring a hold at clean speed at a middling altitude is easy for both pilots, so both can be involved in the subsequent process. This TC left the a/c with the FO as it busily rocketed skywards. The FO will be full time flying, while the TC loses track of it as he diagnoses and talks to the CC.
I suspect the commander got into overload after the initial problems... That applies for all of us.
Yes. So the lesson is to make sure that you give yourself space and capacity to resolve the problem. This is best done by shoving it into a hold at a constant altitude first. For nearly all non time critical problems (and very few are time critical) this is what every Capt would do. Just very odd that a training capt showed such poor problem management.