I don't think this is a case of ignoring the POH. It is just applying a slightly modified technique to unload stress on the flimsy nosewheel for a soft field takeoff.
As said earlier this is different than keeping it off the ground.
The POH of the Tecnam P2002JF I did my initial training on doesn't include anything on takeoff technique(just checked). Neither for paved, soft or short field. Nothing on rolling start for a soft field or full brake full power build up for a short field. And it doesn't describe how to adjust for crosswind either. These are topics for a training manual. Not the POH which describes only the limits and performance.
Just a matter of having the schools write a proper training manual, the authorities verifying the manual and the school making sure the instructors follow the manual.