Generic Deviation Distortion measurement?

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Well, that simple idea came to me yesterday in shower. I don't know if it has been proposed before (i've searched but haven't found anything ), or if it really has some point (it surely has some meaning, but it may be too small). Anyway, here it is:

As the subjectivism vs. objectivism debate is a four-edged sword, i.e. on subjective side - the more pleasing sound may be inaccurate, and ,vice versa, accurate sound may be displeasing, and on objective side - better measuring equipment may be not the best sounding, but at once, we do not completely know if we measure the right thing. So, to rule out the problem of measurements not covering all the mossible distortion mechanisms, and of measurements done on non-musical signal, something has to be done. The idea is very simple.
Get the input signal recording, get the output signal recording, normalise the output (i.e. just divide it by gain value), correct for time lag (not phase lag, just the constant time lag), and compute the mean difference between signals, using mathematical statistics. No psychoacoustics is taken into consideration currently, and there is no analysis, transformation, and simplification of the signal. Some song, or songs can be used, and mean difference calculated.
It is also possible not to calculate only one value for the whole input sequence, but calculate multiple values at multiple timesteps, though that would not be much different from just subtracting input from normalising output. But again, I haven't seen real use of the difference signal in distortion analysis. It's advantage is that it takes everything into account, the disadvantage is that it's harder to find, where is the origin of distortion, but at least it can tell that, say, system 1 is closer to truth than system 2. It can be easily applied to amplifiers, application to loudspeakers is somewhat more problematic - mic distortion has to be taken into account (But as it seems, mics have low enough distortion).

Is there a point in measuring mean generic error of an audio system? Or there isn't really?
 
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