I realize the loss of an engine in an airliner is not a dangerous event. What I'm asking is whether the training reflects that, or whether pilots are expected to secure the engine at double-quick speed.
Slow and methodical is how they want it done.
In the (much newer) 737s that I fly, the procedure for an engine failure at takeoff is, and this is how I brief it on my legs...
"If we continue the takeoff, 'positive rate, gear up'. At 400', track the runway centerline. At 800', we'll accelerate on VNAV, if it doesn't, we'll set Clean Maneuvering. Flaps 5. Flaps 1. Flaps up. Wait for clean maneuvering, set max continuous thrust, then the applicable engine failure checklist."
That gets us to clean maneuvering (likely in the 200 to 225
KIAS range, with the gear and flaps retracted, max continuous power set, and the airplane climbing, from our 800' acceleration altitude, and ready to accept turns to return to the airport. Through all of this, we haven't done a single thing to, or about, the failed engine. It's all been about maintaining control of the airplane and flying the desired ground track while cleaning up and accelerating. The engine is then secured using a read-then-do checklist in a slow, methodical manner.
In the event of an engine fire there are some memory items which can be accomplished as low as 400', at the Captain's discretion, but we'd normally wait until reaching the "applicable engine failure checklist" part above, at which point we'd do the Engine Fire, Engine Severe Damage or Separation Checklist" instead of the "Engine Failure Checklist". Those are the two choices. The former is the only one, of the two, that has any memory items. Those memory items are:
1. Autothrottle (if engaged) ... Disengage
2. Thrust lever (affected engine) ... confirm ... Close
After that, we're back to the read-then-do checklist.