It is correct that the range 5000-6700 K is likely to give a more normal appearance/color rendering than higher or lower K tubes. But it is not necessarily the case. A high K tube may have a higher CRI (Color Rendering Index - the appearance of color compared to the same color in natural sunlight) that a "normal" range tube.
But what the plants care about most it the amount of light delivered to them - so output and reflectors play a big role there. Wattage is only part of it, efficiency and delivery are equally important.
People care about CRI and appearance, plants do not. I am one of those people. You can say and even prove that tube xyz produces the best light for plants to use, but if the tank looks yellow, or blue, or whatever, I will not use it at all. I want the tank to look good to me, and look "natural" to others. If it does not, I don't care how perfect the sprectral match is to PAR (Photosynthetically Active Radiation) or PUR (P. Used R.), it is not suited for display tanks under my care.