It seems to me that there are two schools of thought here, - some were taught the method of engine braking as part of the general control of the car, and this does hark back to a few years ago, but this was also when more drivers actually understood how their cars worked and car control was much more important than the current school of thought (A bit like M&S ... "Plan A (Brakes) because there is no plan B"...) where we see more and more young drivers having really big accidents due to a complete lack of car control. Slamming on the anchors is no substitute for perceptive,and anticipative driving.
In 26 years of driving, the only time I ran into the back of another car was due to :
A) Total Brake failure (A Mini)
B) Complete inability of the ABS to retard the car on a downhill road on ice at walking pace. (A then brand new Vauxhall Calibra).
Personally, I don't think I was ever "taught" this technique, I just gradually evolved it through experience, and it requires a very smooth driving technique to get the best results, otherwise you really might do some damage...
No one in favour of the brakes-only school of stopping has yet answered the question :
What do you do when you have relied on the middle pedal and braked (many drivers too hard and too late) only to hit an unseen patch of water, ice , or oil ?
Answer : CRASH ! Because you have not anticipated the situation and have left yourselves no alternatives or time / distance to do anything else.
I see you causing jams on the motorway due to the on/off nature of this technique every week (red light constantly flashing in the rear window of the car in front...)and some of the jams are the cops having to clean up the wreckage...
Now stop being so naughty and lazy and learn to drive properly, Lol !