Some marketing genius came up with balanced power to help sell conditioners.
Pretty sure it predates audiophile power conditioners becoming a "thing"
Its a terrible phrase because we do have balanced connectors in audio and so saying something is balanced immediately makes anyone aware of this think balanced power is similar.
There are some similarities, like the rejection of common mode noise. That preamp makers make a big deal of being "fully balanced" is not the fault of the tech, but of the hype.
Personally, if I had the money, I'd run 240V from the entrance to the room, and then use a 2:1 balanced step down transformer. This gives you an unbroken chain of balanced power, with high CMRR (common-mode rejection ratio) right up to the back of your electrical gear, along with a very low impedance path. Since 240V transmission takes half the current of 120V, you have less of a voltage drop with long lines. A 10guage cable will seem to have half the impedance. Though I'm on the fence about having such a great connection to the outside power without additional filtration.