Why not batteries instead of power supplies?

The negative side of battery power supplies is the supplies themselves have inherently high output impedance compared to their AC counterparts, leading to higher cross-talk, and potentially weak bass and dynamic range.

This is all theory, of course, as is the benefits of battery supplies. I’m just playing devils advocate. It's not a 100% free lunch, and has its own set of challenges.

I own the Veloce Lithio line stage, which is powered by lithium batteries;  it was a "hot" product a few years ago, and now is rarely mentioned or even on the radar. Vytas, the designer/manufacturer offered an update about a year or so ago which I recently took advantage of--one of the changes is the batteries- now much smaller than the big lithium green boxes that originally populated the unit. Despite this aspect of the design, the unit uses tubes- 6H30s, and I'm using NOS DR Reflecktors.
I have owned the unit for several years and have been very pleased with the sound. It replaced a Lamm L2 Reference line stage, which was also a very good unit. The Veloce lacks for nothing in the areas of bass or dynamics. It is also not noisy- to the contrary, using the Avantgarde Duo, a high efficiency  horn-type speaker with 104db sensitivity, the system is remarkably quiet. 

I think we'll see more of this and Powerwall is just the tip of the iceberg.

But a DC power supply will not get rid of noise problems that originate from inside your house.

@erik_squires, "The negative side of battery power supplies is the supplies themselves have inherently high output impedance compared to their AC counterparts, leading to higher cross-talk, and potentially weak bass and dynamic range."

Well, put.  Weak bass and dynamic range definitely plagues the majority of these products.

@whart, "The Veloce lacks for nothing in the areas of bass or dynamics."

Vytas is a buddy of mine, and your point is absolutely correct.  As a basshead and power focused guy in general, he would NEVER build anything that didn't meet that mark, and took a different tack than what I've encountered in many other products.  As we mentioned Erik pointing out, this really shows up as a problem for most other battery powered products