deefer, you have summed up the issue very well. Can you explain it to sillypeoples?
one thing - this isnt my suggestion. Its whats in the AFM. I'm suggesting that some training organisations bang their own SOPs over the top and they don't enhance the performance of the aircraft - in fact they degrade it. Using the raw data it should become obvious if this suggestion is correct or not and the numbers I've just got from the graphs suggest it does. But we should not forget that using the manufacturers method give more benefits - no (or a shorter) third segment, lower fuel burn (not by much but a bit), less noise (because you will climb better as you accelerate), lower workload in the event of a failure (because you are going faster and are already clean), and I honestly can't see any downsides!
Actually, there is one (just to scupper my own argument). If you take off and climb into a strong tailwind the slightly increased speed (V2+20 as opposed to V2) would mean the gradient is very slightly worse but I cant be bothered to do the maths as the difference will be absolutely minimal and nobody else is bothering to wind the take off path at all so I dont see why I should bother!