That's the most accurate description I've seen!What balanced power does is:
1. It eliminates common-mode E field radition from the mains. I imagine recording electric guitar would benefit from this if nothing else (high impedance circuitry where shielding is not always all that great - even if the cable is alright that doesn't mean the instrument itself is).
2. It reduces voltages to ground. That's why it's used on ships.
3. It eliminates power supply leakage currents from IEC Class II devices with SMPS mains filter topologies originally derived from Class I jobs (i.e. L and N capacitively coupled to secondary-side ground only as the PE connection got axed).
If this makes such a major difference in studios even outside item #1, I do have to wonder how many devices with AES48-2005 compliance issues are still out there in this day and age. They no doubt would still have been very common when RaneNote 151 was written in 1995. Otherwise I don't think there would normally be long runs of signal wires right next to mains wiring that could push CMRR limits in the face of item #1 - right? (This may not even be up to code depending on where you live.)
Just from a live audio perspective, I know of a major world-touring artist that brought their entire audio system to the US. To keep the existing touring infrastructure they used a very large step up transformer so they essentially ran their entire audio system at 240v in the US. That's PA system, mixing desks and backline. By all accounts, the lack of hiss and noise for the PA was staggering. The first comment from everyone on the job was "is the PA switched on?" They had toured the same rig throughout Europe (with no TX) for several months and had become accustomed to the background hiss. I should also point out this was using some of the most modern, top-of-the-range live audio equipment that money can buy.
The guitar rigs also became much quieter, it was especially noticeable with the vintage single coil instruments. This system wasn't using balanced mains just transformer isolation.
If you're ever had the pleasure of staring down a 450ft 48ch analog multicore trying to find hums and buzzes, you'll quickly appreciate how useful mains isolation/balanced power can be. Sometimes audio tx's and pin 1 lifts alone don't resolve the issues. It's definitely not always the solution and it carries multiple risks but for certain situations balanced mains can save the day.