Some mysteries

You have no argument from me on this point.
Although my main amplifier is an integrated in that it has a preamp section and volume control, it has only one pair of inputs, I therefore added an active preamplifier with two sets of outputs and four sets of inputs; what I was not specifically looking for, but have subsequently found very useful is a balance control.
My speaker placement, being constrained by practical domestic considerations, has resulted in the right speaker receiving more room reinforcement than the left speaker which is in a more open location - the result being that with many recordings the soundstage is skewed to the right, a minor trim of the right channel with the balance control adjusts it all back to centre from the listening position, since my head amps also feed from the preamp they too can be adjusted in this way - very useful I find and sod the theory.

@dvv
While I would certainly be most interested at the theoretical level, at a practical level, having no immediate application, it would very likely languish in the collection of useful things I might want to do at some time.
Again, at a practical level, I would imagine it to be more difficult to implement for a head amp due to the generally more limited internal volume for add-in placement and more limited panel space for switch and pot mounting.
WRT calibration and equal signal levels, it is a fairly trivial matter to produce such a recording from almost any thing with a modern PC, free software and a CD burner - or to play such recording direct from the PC or via an external DAC.
Given that PC source is fairly common usage of head amps in the headphone community, this would be more likely their preferred method.
On that note, most soundcards, certainly the better quality, semi-pro types are capable of fairly accurate channel level control - granted that may be more damaging to the signal than external good quality attenuation.
Admittedly, none of the above solutions provide quite the same "on the fly" capability and that IME of my own system, some recordings play best with neutral balance settings but many require balancing, which I usually do by ear and "on the fly".
I suppose what I am saying here is that while I see your point about the mono switch from an absolute calibration perspective, my immediate and recurring use for a balance control is to adjust the soundstage to suit the particular recording. 
So, what I am in fact balancing, is what I hear - which, since it allows for my own hearing imbalance is only distantly related to absolute signal balance.
Who knows, maybe someone out there will build one?
Guess I would like to see your implementation.

Charley Phogg wrote: dvv wrote: @tg  "It mixes both channels together, thus totally eliminating any channel signal difference."   I am sorely tempted to design just such an add-on board. Interested?  Isnn't this basically what cross-feed is? maybe I'm taking it out of context, not understaning the difference,

I could say yes (tongue in cheek), but I would not like to upset cross-feed fans. No Chris, cross-feed mixes left and right channels with decreasing frequency so as to give the impression of a speaker representation of stereo, where the bass seems more omni-directional.

On headphones, without crossfeed, the bass can feel a bit one sided, but this also depends on the balance of the recording and the performance level of the amp.

In the case of this thread, they are discussing the merits of a mono switch which sums both left and right channels - the math being A+B/2 (or more precisely L+R/2)

However, this will not give a true mono derivation because it doesn't give constant power to both earpieces/speakers as would be the case from an already mono signal - it actually boosts the centre information by 3dB, giving rise to a loss in volume of the L-R difference signal. It makes mono-reproduced stereo recordings sound unnatural and has led to the downfall of many an AM commercial radio station, which have become mainly chat stations than music broadcasters to survive.

The only station that was successful in mono AM broadcasting IMO was BBC radio 1, possibly because of the use of a Studer true mono converter? However, such a converter has serious consequences to phase, but that didn't really matter as AM broadcasting is limited to a 4kHz bandwidth, so you couldn't hear the phase problem anyway.

When is mono not mono? When it's derived from stereo by way of the simple A+B/2 mono switch that featured so prominently on so many older pieces of hi-fi equipment (that's why we hide ours [where fitted] round the back). Personally I wouldn't bother - a mono switch on a stereo piece of equipment is only of use when playing a real mono source.

I really hope nobody takes me to task about true mono because it may take me an age to find the mathematical argument I had to formulate many years ago to prove the case.