Well, I agree with you that nobody moves naturally as if they were stiffly moving without trying to bump their head on a ceiling. If a person were to move with such rigidity, surely they would have a loss of power, but not so much due to the flat line as to the stiffness with which you describe this movement, in this ceiling analogy.
I didn't see the flat line movement described that way by those were are practicing it. If they did, I'll defer to them to respond.
I just saw them say move trying to keep your head level. I can only imagine that this is said to keep a level plane, but I cant imagine it is done with ridigity and stiffness to the point you describe in the ceiling analogy.
It's the same as poorly performed sinewave motion. Incorrect practice of SW could theoretically also lead to loss of power... or if nothing else, to not maximizing power.
I will defer to those practicing that way to take it further than I have, for I am not schooled in that manner. However I simply suggest that flat line movement, sinewave, is not going to make or break power on some TKD movements, as the movements do not exclusively derive their power from that motion to begin with.