I've thought about this same kind of thing. I happen to have the DTS surround sound software, and could assign 4 tracks to 4 channels and then listen to it in the living room on the movie-oriented surround sound system. I even gathered 4 AT853's figuring I could make a more-or-less coincident quad setup on the cheap.
Then I asked myself "when would I actually use it?" I had to face the fact the answer was, in my case at least, "not very often". 99% of the time I want "what's going on up front", and I really am trying to ignore "what's going on behind". I can't envision many cases where it would be useful to mix in mics pointing backwards.
Surround would be wicked cool in 3 instances that I can think of.
a) the standard bluegrass thing of huddling around 1 mic. I don't tend to hang with that crowd much, so it wouldn't happen often.
b) Halloween a few years ago, Gov't mule played Pink Floyd music and had rear surround speakers and sound was swirling around the room. It would have been cool in that case, I could have captured that and played it back at home, but I'll probably never be at a show like that again.
c) nature recordings. if you could go out in the bog with frogs peeping in every direction, it might be cool. But I would need 4 really quiet, matched mics (better than AT853's). not in my budget.
As far as 4 mic stereo mixes with mics pointing forward... I know a lot of people do it, but I'm not a big fan, and I definitely wouldn't do it on the fly. Maybe people that do it see themselves as a great chef inventing a new recipe, I'm not sure. Maybe they really are better at it naturally than I am. I dunno. I think it generally introduces lots of phasing issues. Every time I've tried mixing 4 mics in post it, I came to the conclusion that one of the solo tracks sounded better than the mix. Even stage lip mid/side with split omni flankers... I always pick one or the other. Of course, there is always one exception... one time, I think Hunter Mountain 2008, I ran Senn ME66 guns plus small omnis (Church?) and the sum was better than the parts. But that was just because I had 2 extremes which were poor choices on their own... a proper set of cards probably would have been best in the first place.
As far as running 4 mics, and not mixing them, just because you can't decide what to run that night, I'm a big fan of that. I'll run ADK-TLs cards and AKG483 hypers, and when I get home I decide which I liked best. If it's a good room, not too boomy, I'll probably like the TL's source. If it's boomy, I'd probably like the 483 source. That helps educate me on what do bring the next time, and so on.