You know - I see all these posts about "the device should be transparent or something's wrong" and it's quite frustrating. I mean, why is anyone in this business? Why is anyone continuing to develop new products? Is the implication that all devices are transparent and there's nothing better? Seems like that's the same as buying a single product, then shutting your eyes (or ears, as it were) and never looking at anything else again. I guess that works to save money, but you miss an awful lot while your head is in the sand down there.
Back to the original question: with headphones, it's never just about power - it's about
clean power. This is similar to amps, too. If it wasn't all about
clean power, we'd all be sitting here with our $1000 headphones plugged into the run-of-the-mill receiver headphone jack. That's because the detail offered by a typical receiver might be as good as one can get
if you've never listened to anything else. (Yes, there are some receiver-headphone combinations that can be quite good, but it's the exception rather than the rule.) Instead, headphones offer an ability to discern and enjoy
detail at an extreme. Most of us find that equipment optimized for headphones sound much better than an all-purpose receiver. So, headphone amps are used and DACs. Detail is the key. In order to provide that detail, the power supply must be
clean - very clean. It it's not, then the noise from the power supply injects signals into the music that aren't supposed to be there. Or, the noise combines with the music signal to increase distortion. Either way, details are lost and the fidelity to the original recording is not what it should be. This is extremely important in DACs, because as the source - the music signal is at the lowest point in the amplification chain. Any lack of detail or defect is amplified many times over.
One might suggest that portables with batteries overcome this, because the batteries are pure DC. The problem is, that DC varies all over the place as the battery loses charge. In addition, compromises are made to preserve signal swing (voltage differential) and running time. These things mean that a portable is not going to compete with a desktop in every category - DAC or Amp, either one. As for DACs, USB-power has similar issues. I was long a proponent of USB-powered DACs, because of the convenience and simplicity. As with some of the posts above, most everyone assumes that if the power/current requirements can be met, the rest is trivial: It is NOT. Only a desktop (or equivalent combination) can offer a power supply down into the microvolts of noise, which enables the maximum performance available from the particular DAC chip - whatever it is. Some desktop DACs might be externally powered, others with their own transformers. Some very high-quality DACs may require more than one transformer in the case because the connectivity section might require one voltage, the DAC another, and the output stage still a different voltage. It becomes a little difficult to provide all of that with several walwarts. The use of transformers can increase the detail capability of clean power by optimizing the power supply in each section.
As with any audio device, the quality and performance is usually commensurate with price. There are always exceptions, but to claim that all
quality-implemented DACs are simply transparent is missing the point.