Yes, Darren, you are right.....!
Battery power seems ideal, but there are issues. They are related to the chemical process of conversion; a lead and a lead dioxide plate combine with sulphuric acid to produce a reversible reaction generating water (pulling back the SG of the acid electrolyte as it discharges) and lead sulphate (which deposits at the molecular level on the plates).
The issue is speed. While a lead acid battery can deliver low resistance, down to tiny fractions of an ohm (it is common, for example, to fit automobiles with 1.5 hp electric starting motors, easily driven from a simple 12V, $80 lead acid battery) the conversion from chemical to electricity takes a bit of time and starts to peter out at around 10KHz.
The second issue is the inconvenience of having to disconnect the battery from its SqueezeBox, connect it to a battery charger, and charge it slowly over a long period so as to prolong its fairly short life, maybe five years if you are very lucky.
Now, 10KHz is an audio frequency, and it means you need to use a large, fast bypass cap across the battery to keep the impedance low at higher audio frequencies. Of course, you have to do this on a standard AC supply to act as reservoir and filter the AC, too, and when you look at the inconvenience of the battery, the cost, the chemical hazard and the weight, you realise that maybe a trafo ain't so bad after all.....
The need for power supplies from AC is ubiquitous, and the large semi companies have produced very good regulator chips for years now which are getting faster and faster and delivering pure, clean DC.
They still do not have the impedance characteristics required for really good audio - my opinion only - but they are outstanding as pre-regulators. The LM317 and the Linear Tech chips are very good, and will deliver very accurately controlled voltage with zero ripple over quite a range of currents. Wayne exploits this very elegantly in his Ultimate power supply, which now has an Aspen Nirvana regulator in it in the premium version, and yes, Bill, I did design the supply for speed, but also for negative output impedance across the audio range.
Cheers,
Hugh