midside, the CMTS stereo microphones used specially adapted matched pairs of MK 6 three-pattern capsules from the CMT series. I owned two of these microphones at various times back in the 1970s; they were manufactured through most the 1980s, even after the rest of the CMT series was discontinued.
An omni can very well be the mid microphone for an M/S pair; given unity-gain matrixing, you'll have the equivalent of X/Y cardioids. I'm no great fan of X/Y cardioids myself, but a lot of people sure use them, so I hope that this helps explain the design choice. Also, stereo microphones in general are occasionally used either as a "failsafe" way of "backing up" the placement of a single microphone (imagine if you were miking a world leader for a live broadcast and one channel went out for whatever reason--a bad cable, perhaps, but there's no time to find out. You can't exactly interrupt and say, "please hold on a moment while I get another microphone"). Finally, there is a technique called "Straus-Paket" recording in which the signals from a concident cardioid and omni are recorded onto two tracks, and then the mix between them can be varied during playback to produce any result along the range from cardioid to wide cardioid to omni "retroactively."
John Willett, some figure-8 microphones are not well suited to be the "S" microphone in an M/S pair. Some Royer ribbons (not the ones they sell for classical music, but some of the models that are more "pop" oriented), for example, have different-sounding fronts and backs; the company admits this freely, says that it is an intentional aspect of their design, and recommends using one side versus the other for different applications. That's certainly one approach to marketing, but it would make me think twice before using that type of microphone for M/S.
However, please note that all the polar diagrams which you reproduced showed no difference whatsoever between front and back below 16 kHz--and 16 kHz is at the upper limit of the frequency response for this type of capsule. Furthermore, since the the published curves of different manufacturers are not drawn the same way, they cannot be compared directly; we must still compare actual microphones. But mainly I object to the fallacy of presenting a plausible explanation for a proposed phenomenon (a "back story," if you will) as if it were any evidence that the phenomenon itself is real. This fallacy is so rampant in the audiophile universe that I have become quite allergic to it. I'm sorry to be "getting on your case" but you made an overly categorical claim, and while you've said many interesting things and you clearly do "know what you're talking about," you still haven't backed up your claim with any particular evidence about actual microphones so far. That's what it would take, I think.
--best regards