During flight training, pilots are drilled very frequently in doing essentially exactly that. The instructor will suddenly decrease the throttle, then announce "Okay, you just lost your engine. What are you going to do?" In my experience, this simulation will only happen when "at altitude" -- safely high enough to disallow any real risk in case the engine fails to spin up again.
Airline pilots are fortunate enough to have very realistic simulator training that can reproduce the situational context effectively. But, this isn't the case for primary flight training. So, no instructor is going to execute the above drill immediately after taking off when still low to the ground (the situation that led to Appleton's crash).