KLowe, thanks for the reply, and yes, listening to the "S" signal alone is instructive but not musically satisfying, and the general public shouldn't be exposed to it. It's kind of like, if you're a surgeon you can look at people and imagine in full color what their insides look like--but most other people don't like to hear chapter and verse about that, especially while eating.
I don't know whether people know how stereo FM broadcasting works, but it's just like M/S. The left and right channels are combined 1:1 and are broadcast as the main (or mono) signal. At the same time, the difference between left and right is derived by matrixing, and this "difference channel" (which corresponds exactly to the S channel of an M/S recording) modulates a 38 kHz subcarrier which is then demodulated in your FM receiver when it is in stereo mode--and the resulting signal pair is matrixed back into the original L and R signals. (Voila.) Mono FM tuners (which used to exist--my father had a nice McIntosh one in the mid-1950s) simply didn't have the subcarrier circuitry at all. For a while you could get add-on "stereo adapters" for mono FM tuners, but I digress.
In FM broadcasting the entire process has standardized gain settings, so there isn't generally any reason to adjust the matrixing parameters in your FM receiver. But as you know, sometimes stereo FM reception in fringe areas can be noisy, so some receivers have a "blend" control which reduces the difference channel and/or turns down the treble in the difference channel, thus preserving some L/R separation while reducing the apparent noise. That is analogous to processing the S channel separately before dematrixing.
With digital recording you can assume that the channels are quiet enough, so any adjustments you make will more likely be to improve imaging (increasing or decreasing spaciousness, as I mentioned, by playing with the S channel's low-frequency response) or tone color (reducing the sharpness of a peaky microphone for example, or making speech more intelligible, both of which can be done by equalizing M).
One important thing is, with a proper setup the S (or "difference") channel should never contain any direct sound that isn't being picked up in the M channel as well. If it does, then either you were miking too closely, or the pattern of your M microphone was too narrow for the stage width of whatever sound sources you were recording. It should always be possible to hear all the program material in the proper balance by listening to the M channel alone (in mono, of course).
M/S was introduced in the 1950s as a bridge between mono and stereo. The engineers who used it had all been picking up sound in mono for years, so they knew how to place a microphone for that purpose. The S microphone was then added on in the same location for compatible stereo recording/broadcasting. People who intend to record a lot in M/S, and who are sufficiently fanatical (in which case they are all immediately my friends), might want to practice making mono recordings that sound good, as a kind of preparatory exercise--it's extremely instructive, and a cool skill in its own right.
If you followed what I said about FM stereo--theoretically it would be possible to broadcast a live stereo pickup over FM by modulating the main carrier with the signal from the M microphone and the stereo subcarrier (the difference channel) with the signal from the S microphone.
Does that make sense?
--best regards
P.S.: I can't resist adding that in stereo LPs, horizontal groove modulation = M and vertical modulation = S; the 45/45 degree design of phono cartridges functions as the M+S/M-S matrix. Some moving coil cartridges exaggerate the M-S pickup, which gives more "air around the sound"--a characteristic that many audiophiles like. Carver used to sell a little processor called the "Digital Time Lens," built around an M/S matrix pair, that made digital recordings sound as if they were being played back through a cartridge like that.