@carlsbad Don't be so negative. With most amps engineered to run on AC, one issue is the need to convert from DC. But apart from this, I doubt there would be difficult problems once suitable batteries are sourced. Far less difficult than getting rid of noise on the mains. And less costly probably.
But no I haven't implemented. I've thought about it and am doing so more currently (sorry!). Dedicated battery power supplies for pre-amps and phono amps have been around for years. Running only them certainly improves SQ by eliminating noise on the mains at a stroke. Certainly turntables can and some do run on battery supplies although, unlike some, I very much doubt mains noise finds its way to the stylus.
Having wrought some big improvement already at cheap cost, that leaves us with power amps. I have read of powering single-ended flea-power valve amps on batteries, reporting positive results. But up to now running my big Class A Krells has put me off researching battery power because suitable batteries have not been in the mainstream. But now I am guessing they are readily available given booming power tool and car applications No-one could deny a car battery could easily run a big amplifier. With my Krells it is noticeable the big draw is on switch on when the big capacitors are filled within a few seconds. That dims the room lighting momentarily. But once full, the topping up process draws a lot less amps.
@carlsbad you have strengthened my resolve to start serious work. Eliminating mains noise is certainly a very attractive proposition.