Hello,
For opamp based amplifiers, the quality of power supply means much less than discrete amplifiers. In fact, you really don't need sophisticated regulation system for opamp based ampliifers.
This is because opamps that WE (HeadFiers and HeadWizers) recommend have very high supply ripple rejection over very wide bandwidth. Also, the inputs are designed so that normal noise coming from supply is very unlikely to escape to the signal. (Given you don't connect output to rail with a resistor.) Although this system is not as good as LM317 and other specially made regulators, this makes a life extremely good for power supply designers and builders.
Battery use will give you less ripple. However, there are problems too. It is very difficult to find suitable high voltage batteries. 9V batteries has relatively small current per hour rating. People stack many batteries to achieve high voltage, but doing that will increase the supply impedance which necessitate the use of ground drivers. Also, you cannot pull too much current off of batteries.
And, last and the most importantly, you have to recharge. ... I hate recharging time. I wanna turn on my system whenever I feel like and be able to listen. I wait all day waiting for experiments, people, phone calls, compilation, printing, copying, etc etc. When I am off work I would like to avoid that if I can.
Yeah lots of pluses and minuses. What I do is to use battery if I have to build a portable amp. Otherwise, I stick with outlets. I found it very interesting to work with AC and have gotten superb results. I say battery operation isn't all crack out to be considering the negatives.
T