Um, guys - a couple of points here...
1. The pythagorean theorem is NOT the square root of the sum of the squares times two, it IS that the hypotenuse is equal to the square root of the sum of the squares. The "times two" factor comes in in reference to defining True Position which leads to Point 2.
2."In this case, multiplying by 2 to yield a number that is twice as large as your deviation from nominal won't tell an
engineer or toolshop how far and in what direction a surface needs to be moved (corrected) to meet the original profile specification." Yes this is true, but in fact what you are doing with profile is the same thing you are doing with True Position, you are reporting on the total band that the deviation fits into as compared to the total tolerance band. Just as TP alone won't tell anyone what the direction (i.e. vector) of the error is but rather only it's total magnitude, neither will profile, that's why you have to additionally report, in the case of TP, the X & Y values (or Y & Z, or X & Z) in order for clarification, just as you have to additionally report locations of individual points and/or surfaces to clarify profile.
So, the bottom line is that you have to correctly report profile, just as you have to correctly report TP, or Perpendicularity, or Angularity, but in addition if you want it to make any sense to the people that have to either fix it or make a decision as to whether its acceptable or not, you have to provide additional information for the analysis.
My pontification ceases....