Why not batteries instead of power supplies?

I heard a system with the Veloce linestage and it sounded quite good.  I have no idea how it would compare with an otherwise identical model running off of a conventional supply.   I have also heard an ultra expensive version of a preamp that is quite similar to mine (same builder), but it ran off of a large battery pack.  It too was very nice sounding, but, it had to be recharged quite often.  It, like the Veloce, is a tube unit.  I saw pictures of a DIY tube phono stage with a battery power supply that was the size of a large refrigerator; all in the name of extremely low output impedance.

I would think that battery power would make even more sense with solid state where there would be far less draw at idle.  

Jeff Rowland Design Group offer battery powered amplification since early 90's

http://jeffrowlandgroup.com/us/preamplifiers-criterion.html

http://www.hifi-advice.com/blog/specials/jeff-rowland-company-special/jeff-rowland-battery-power-sup...

@nycjlee +1! Vinnie Rossi room was one of my fav at LA Audio Show this year!
Sutherland battery-powered phono got ditched by the man, I was really disappointed that in his interview with Stereophile he bluntly refused to answer why.
Agree with the sentiment that God is in listening: PS Audio Power Plant worked magic in my lab when we tried to make video of our efforts. When used in my "bedside" kit of Naim CDX/Lehmann h/p Amp/HD600 the benefits came at the price... Sent it back to the lab!!