So, anecdotal evidence is the accepted norm, then? I don't doubt that something may sound 'better' to you, but there is absolutely no objective proof of that. What may sound better to you will not sound better to another. And I'm sorry, but I don't see the point of being respectful about the belief in magic.
More expensive gear does not better performance equate. It can. But it definitely does not broadly correlate. Besides, we are all aware of valves and solid state, and NOS and R2R configurations, many of which actually perform sub-standard against industry measures, but by which people swear.
'Sounds better' is, in 99% of cases, nothing more than subjective opinion. Any amp that has enough current to drive a headphone to the level at which you listen and do it with low distortion will sound best. You may like the distortion, you may even like frequency fall offs, or ramped IMD, BTW, which the AK240 is ought to do, but that doesn't make it 'better'. It makes it more in tune with your preferences.
The PS1000 is no different: if it is being fed enough current at the right voltage level, that's all it needs. DACs follow similar rules. And I agree, not every good measuring DAC I actually like the sound of. But that means nothing regarding sound quality.
The PS1000 isn't a hard to drive headphone. A lot of gear is more than up to push it to perfection.