I don't know that I want to debate with the person that has probably done more multi-mic recording and mixing than anyone, and this sounds like justink's opening, but --
I don't know that I'd say mixing 2 stereo pairs is necessarily a bad thing or can't be done. For instance, I'm pretty sure using a coincident stereo pair of either XY cards or MS is a variation on the Decca tree arrangement.
I will say I've been attempting to mix a center, near-coincident cardioid pair with a pair of spaced A-B omnis for many years now. With the exception of multiple mics onstage, this is really the only way I've tried to mix multiple mics. And I should say, this has always been done at outdoor shows. And at that, I've only done it for large outdoor shows, say 8-10K people or more.
Overall, I'd agree with a lot of the comments that 2ch is often or even generally better. I have had a handful of times where I definitely like the 4mic mix better. For me, the hope was to get a larger, more spacious soundstage from the split omnis and get the fuller low end from the omnis that don't have the proximity effect of the cards, but have the center card pair to ground things and make sure there isn't a hole-in-the-middle effect. The few times that it "worked", I feel I got this, and I liked the 4ch mix better than either 2ch pair.
For me, this emerged after doing a lot of outdoor, omni recordings, either with a j-disk or with split omnis. Generally, I didn't feel I got enough stereo separation with the j-disk, and split omnis generally seemed to have a hole in the center.
So, that's the attempt, and what I think I'm buying. In terms of specifics, a lot of it has to do with the fact that I keep running my generally preferred near-coincident card pair, so I always have that to fall back on as a 2ch recording -- no downside in attempting the 4mic recording. From a mixing/phasing/whatever standpoint, I realize that I'd be better off with XY cards center, but I don't prefer the sound of that as a 2ch recording, and I don't want to risk screwing up my fallback 2ch recording. Same thing for why I don't want a single card in the center or a single omni center with my flanking omnis (so something like Decca), since I still want the option of having my best/favorite 2ch card recording as an option.
On your 3mic suggestion with a center omni: That seems like it could be good for traditional acoustic recording, I'm just wary of it as recording technique for amplified PA music. Typically, the mix on a PA rock show has very little panned left and right, with most of the music panned pretty close to the center. (At least, I'm thinking here of the large outdoor shows I use 4mic recording at -- individual instruments and guitar cabinets add little in this case to the overall mix, it really is just the PA.) So there is very little natural soundstage to be found -- putting an omni as a single center channel would seem to me to then just keep the recording really panned to the center, unless you kept that pretty far down in the mix (in which case you lose the benefit of the extended low end of omnis).
As an aside, I think using a 1.5-3m spread with A-B omnis pretty much does the opposite -- on playback it creates an unnatural separation, really highly exaggerating the stereo spread, driving the sound to either come from the left speaker or the right. Done to record an actual orchestra, this would probably sound horrible, as the stereophonic zoom would indicate. With a very center panned PA-driven concert, it helps really make a bigger and wider soundstage than the PA was providing at the event (due to the center panning), but it also makes for a hole in the middle effect as well. You could correct the hole in the middle effect by only splitting the omnis 0.5-1m, but then you would keep that center-panned soundstage of the PA stacks. I think when I've got my 4mic attempts to work, it creates a bigger sounding soundstage with the wide split omnis, and then fills in the missing center of the image with the cardioid pair.
All that said, I've just recently come across the Optimum Cardioid Triangle technique. I've been thinking I might want to try that out, though it violates my policy of not arranging my mics to keep a 2ch "out" that I can always fall back on. I might try to do a split A-B pair of forward facing cards, with one card as the center on the OCT, and then the side facing supercard pair of the OCT. That way I can mix the OCT attempt and still have a forward-facing A-B cardioid pair to use as a 2ch recording if I don't like the OCT.
OCT though does seem interesting to me, in that the side-facing supercard pair seems to do what the split omnis do: make an exaggerated stereo spread, with I hope would help with the typical center-panned PA system.
Gut -- what was your experience with OCT?