On the 737, if one choses to use full climb thrust, which is advised for fuel saving whenever an unrestricted climb is expected, it will pretty much always be higher than reduced take off thrust.
Apparently Engine life is not reduced by using full climb thrust after a 40% reduced take off.
NADP is just a profile, it says thrust reduction, as that was the normal thing to do for a very long time. However with todays engine apparently it is not longer the case.
One can fly NADP with fully reduced thrust, which actually increases the noise footprint farther out as the climb out is slower compared to full thrust, while still meeting the minimum gradient. Absolutely legal, as is increasing thrust at thrust reduction altitude.