It's not an argument I would recognise as relevant... By balanced I always mean differential and would never consider it meaning anything else in the context of signal transmission.
In actual circuit topologies there are all sorts of ways of looking at things and with some room for contention!
An op amp has a differential input and can provide pretty amazing CMRR but most have an unbalanced output and deal with the signal in an unbalanced form after the input long tailed pair (LTP)....
Or do we mean a circuit in which + & - inputs are amplified by two identical amplification circuits from input to output with the output of course also balanced but the only CMRR as such being provided by the matching of the two amplification chains? Where then should the cancellation of common mode signals happen? At the speaker as in your set up?
A bridged amp is of course both balanced and differential
at the output but may well have an unbalanced input... this may be converted to balanced by a handful of op amps or the amp could have intrinsically inverting and non inverting power amps for each channel (yes two power amps per channel. Normal for bridged). Done well this can completely remove speaker return currents from the main ground, with obvious advantages... at the expense of using twice as many parts....
It's an interesting subject with many pitfalls for the unwary and gotchas... I have some examples of my own work where in trying to use a particular topology for a certain reason, but keeping it truly intrinsically balanced, I've designed almost to the "you've wallpapered over the door" stage and it's gotten maybe 10 times as complicated as envisaged in order to design around certain gotchas that would never have occurred if it was unbalanced!!
Do we want end to end balanced? From say MC cart to speaker where it finally joins the two anti phase signals? Consider the relative proportions of the differential and common mode signals for a moment... and what would happen if the common mode signal clipped... especially asymmetrically... nasty!!
This is why I said in an earlier post that the best balanced topologies usually have a certain elegance to them
And all the above is just scratching the surface of the subject, so dear reader, you may imagine my thoughts at "so what's all this phono V XLR plugs. Which ones best"