Switching to battery power

Yeti, but they are 'relatively' expensive, but provides a pure sine-wave

My ASR Emitter II Exclusive power amp runs off a battery that's charged by two power supplies. The sound is so clean that my other components are only filtered by a PS Audio passive line conditioner and some Akiko Audio tuning sticks. Milwaukee makes a lithium battery generator that produces a pure sign wave. Here's a review, https://audiophilestyle.com/forums/topic/60304-surprising-budget-audiophile-product/

My new DAC uses super-capacitors that are said to act like batteries.  When I go from stand-by to on, it takes a bit over 2 minutes for the super-capacitors to charge.  Why don't designers use these more?

I use a Thales turntable and have never been happier.

I have never heard ASR but a friend whose opinion I highly respect on these matters says it’s the best sounding integrated out there. 
(Both Thales and ASR are battery powered)

Running very low level devices like phono stages off batteries makes sense. Channel D does this with several of their phono stages including the $60,000 Seta L20. The AC charger is switched off during operation. 
Otherwise, there is no significant benefit worth the expense. We have excellent power supplies.
In theory since a really big battery is a really big capacitor you could build a very powerful amplifier around one. I am no expert in this but it seems that the cost and size of such an amplifier are prohibitive as nobody seems to want to make it.