Unless I'm misunderstanding your question, Stereophile already measures amplifiers with 1khz and 10khz squarewaves. And, I agree that this is very useful.

Though it might be interesting along with seeing the relative levels of the odd harmonics, I don't think it would be too useful.
The square wave time/amplitude display along with the other measurments provided (freq response, harmonic and I.M. distortion) are better more specific methods.