This doesn't take in the fact of losses through transfer from water storage tanks and the variable temperature of the hot and cold water storage tanks refilling from their respective supply when water is drawn from them. This can never be taken as constant.
A shower outlet will only allow a certain amount flow rate no matter at what supply pressure (all the little holes in the head can only take so much) so the shower should be set to allow optimum flow from the actual outlet. This reduces the effect of it actually choking itself with excessive push back forces (the equal and opposite forces thing).
The temperature of the hot supply should be set 12 to 15 degrees C above normal body temperature (37degrees C or 98.6 F) to allow for blending and to give a variable control for differing personal needs and wants, but never being allowed to get to the point of being able to scald the skin. As we age, we lose the ability to regulate temperature properly, so it is safer to have the maximum temperature of the supply set to a safe and with standable level. This applies to children as well.
The pump used should be fixed to allow an output of only a third of the volume of the water that is supplied to feed it. This reduces the possibility of the pump ever running dry by emptying the supply tanks. The tanks should also be set to allow an output of only a third of the volume of the its supply. Pumps should always be supplied from tanks which allow the water to settle and become still before being drawn off to the pump. The stops the effects of aerated water being drawn into the pump and causing spluttering of the water at the outlet due to the build up of trapped air within the impeller. This also reduces the build up of scale within the pump and mixing valve by keeping a constant flow of water and not a mixture of air and water.
Yes, you're right, it is amazing what you think of while standing in the shower. :-))