I'm afraid we will have to disagree.
On a Boeing, simply pushing the thrust levers forward is absolutely NOT always correct, or advisable! (Though it is on an Airbus, that so many seem to decry!)
Try doing that on a coupled approach, with a decision height below 50R and see what happens.
OK, I focussed on the thrust levers cause that was the discussion topic. Lets try this:
I believe pilots should be trained to always manually establish the climb by pulling on the yoke and pushing on the thrust levers while pressing the TOGA switch when doing Go Arounds/Rejected Landings in Boeing products. It does not matter what the autopilot and/or autothrottle mode is, what the protection modes is, what functions are inhibited, or anything else; the result is the same: you go up, away from the ground, and you accelerate. Once it is established the aircraft is climbing and accelerating the pilot can clean up the configuration (raise flaps/gear). Only at that point should he allow the automatics to take over to finesse the climb. Again, this is for Boeing products only. This will not work for Airbus products. (And again, this is not necessarily "bad" and I am not "decrying" anything. This is "different". I'm old school and personally like that Boeing difference because it meshes with my military training. Others may prefer the Airbus difference.) So my point is that if your operation is using Boeing products, I believe you should train your pilots to be old school and fly the airplane like a pilot, and not like a system operator keeping track of modes and inhibition logic for every possible combination of events and scenarios.)