... The 6dB increase in volume only occurs if the balanced line standard is ignored ...
Yes, you’ve pointed that out previously. That’s why I specifically mentioned Audio Research in my example, because that’s the equipment I use.
The 6dB improvement in signal to noise of the gain stage is theoretical
In my example of ARC, it’s listed in the specs, it can be measured and - most important - it can be heard. It is very, very real.
I see the really big advantage of balanced lines in that you don’t have to have an expensive cable
Yes, that is a potential advantage. As we’ve previously discussed, it’s not the only advantage, but I understand you feel passionately about it.