First, I do not take ANYTHING as "absolute truth"! If I did, why would my assessment include the word "about"?
Second, I have seen takeoff thrust below climb thrust maybe 50% of the time in our 748 fleet. Just had it again today. Happens less in the 744 fleet, but still common (25%?). Since the B5F engines have higher standard derates than the B1F engines, Derate + Assumed Temp tends to push a more significant TO thrust reduction with the B5F engines in the 744.
As for your "why..." questions, the answer is relatively simple. First, Boeing and Airbus do not normally weigh in on engine operation as much as GE, P&W, CFM, and other ENGINE mfgrs. Second, those engine mfgrs want to make as much money as possible, so they will not likely recommend operations that decrease their bottom line. Third, the airlines are slaved to their engine lease/maintenance contract terms. When those terms are structured around an 'average TO thrust reduction', the airline will adapt their operating procedures to minimize their costs within those contracts. That is, they will strive to achieve the MAXIMUM average TO thrust reductions possible in order to pay the minimum for their engines/maintenance. In order to achieve those 'averages', they will dictate maximum derates + assumed temp reductions for as many flights as possible.
As for 2-engine vs 4-engine performance, remember that max engine thrust is predicated on specified performance with 1 engine inoperative. Therefore, a 2-engine airplane has to demonstrate performance on 50% total thrust, while a 4-engine airplane has to demonstrate the same performance on 75% total thrust. Therefore, each engine on a 2-engine airplane has relatively MUCH higher performance margins.
Finally (for now), basic physics has not changed much in 3 years. While advances in metallurgy and composit materials have allowed operations at much higher temperatures (or G forces), the relative stress-strain relationships at/near those limits have not changed so much. Plastic deformation still occurs at an exponentially increasing rate near the demonstrated limits of the material. Low-cycle fatigue is still a major factor in airframe and engine life; the materials allow higher stresses for the same lifetime, or the same stresses for a longer lifetime. The 50% material margin is still the benchmark,
AFAIK.