I think you measured using a single frequency at steady state response at one 1KHz.
That would be wrong. Here is a full frequency sweep of the P12 Powerplant:
Full frequency sweep is performed from 20 Hz to 20 KHz.
It might not reveal the affectiveness or deficiencess of the power plant.
Seeing how the above measurement showed that the P12 increased noise instead of decrease it, I say your assessment is incorrect.
A better test would be using a square wave input then look at how the output follows the input square wave with different load - using high current and low current load. This would be a more difficult test than steady state.
That is still "steady state" by your definition since there is no discontinuity in the signal. That aside, you can't have square wave as a valid audio signal since it has infinite bandwidth (Fourier Theorem).
Also make sure the partner amp that you’re using for the test is not the limiting factor. An outlaw amp probably is not really a good candidate. You probably need a better amp.
The amp was not the limiting factor if you read the review of PS Audio P12 Part 2:
Here is the amp by itself, with continuous power and burst:
Now see how power lowered while using the P12:
Both burst and continuous power reduced. This was easily explained due to use of current limiting in P12, contrary to company marketing and understanding of their CEO and founder.
We can see this in power sweep as well:
I think the flaw of most of your testing is because they are done in the frequency domain.
Your thinking is wrong. All testing is done in time domain. The graphs are shown in frequency domain since it is hard for a human to tease out the noise and distortion from a waveform display in time domain. Keep in mind again that based on Fourier Theorem, time and frequency domain are interchangeable.
Frequency domain also has a major advantage in that much of our psychoacoustic knowledge is in frequency domain due to how our ear works with a bank of auditory filters.
Bottom line is that P12 is not a true power regenerator and has current limiting which reduces performance of amplifiers. Testing clearly showed this. With non-amplifiers, it simply did nothing useful since those products have their own internal filtering and run on DC, not AC.
Note that company doesn't provide any of the measurements I provided. Had they done this type of testing, they would have a) seen the degradations P12 introduces and b) realized it makes no difference to output of audio products.