I have a lot of requests to make CMOY's that have DC jacks so that they can be plugged in. I understand that certain applications may require a DC power supply, particularly if the amplifier will be on all of the time. If this isn't the case I will argue until the end of the world that if the device has low enough power demands battery power is a better way to go.
First think about how an amplifier works, and do so by looking at the wikipedia definition of an amplifier.
It does this by taking energy from a power supply and controlling the output to match the input signal shape but with a larger amplitude. In this sense, an amplifier modulates the output of the power supply to make the output signal stronger than the input signal."
Since we are taking energy from the power supply and using it to make a controlled output it would make sense that the cleaner, or closer to a perfect DC power supply we can get, the more accurate our output will be.
Considering DC Power Supplies
Several steps usually take place in a DC power supply like those used in small audio amplifiers
1. Step Down Transformer: A transformer steps the AC power down from the wall voltage 120v in the US to whatever the desired voltage is. At this point we still have AC current in the form of a sine wave at a lower voltage
2.Rectification: Using a recitifer Alternating current is converted to direct current. Unfortunately this is really just taking the part of the sine wave that goes below zero volts and making it positive. Instead of a constant DC voltage we have a constantly moving DC voltage
3. Filtering: Using capacitors and other passive components this bouncing positive DC voltage is now filtered into a flatter, but still not perfectly flat waveform
4. LDO regulation: Generally small signal audio amplifiers will employ a LDO regulator to regulate the bouncing waveform into a much flatter, more constant voltage DC output. LDO regulators are notoriously inefficient and cannot perfectly remove all noise from the system.
All of these steps and you still have dirtier power than using a battery or two. Cheap DC power supplies, the kind that come with lots of entry level equipment often have easily audible noise in their audio output. Also think about the cost involved with all of these steps. Transformers, large filtering capacitors, and regulator IC's are all expensive components, often the cost of creating clean DC power is a huge portion of the overall cost of amplifiers. Which is why if you have a device, such as a headphone amplifier that uses very little power why not take advantage of the fact that you can use a much cheaper, better performing power supply known as a battery. I highly recommend the tenergy centura brand rechargeable 9V batteries which can be charged and recharged over and over again yet still feature all of the benefits of a battery powered source. We aren't the first people to think of this, there are several high end phono preamps and headphone amplifiers that utilize battery power to more accurately amplify.