Oh, boy. This topic can be a real bag of snakes.
A mono recording is much closer to how people actually hear and process sound. Our two ears allow us to determine the direction of a given sound, and because sound can't reach both of our ears at the same time, we get spatial information.
Just like a single microphone.
Sure, there are plenty of amazing stereo recordings from Alan Parsons, Pink Floyd, etc. But as time goes by, the recordings I come back to the most are the ones where you can hear the band playing in the room together. You can really hear the difference in phase, coherency, etc. of the recording.
20+ years ago, I remember an article in Mix, where a guy had converted a Studer 2", 24-track rig to mono. He dropped in a full-width head, and kept the tape speed around 30 IPS. I seem to remember the numbers being staggeringly good. However, I don't know that it was ever used outside of a lab setting. Does this ring bells with anyone?
In short, if we are talking about making a stereo (or in the case of Ambisonics, surround) recording using a single microphone, or going to a three track style recording (see below), I'm in. Otherwise, I prefer mono.
To address a couple of things in the OP, your three channel recommendation is almost what three-track systems originally were. Mostly used for classical recordings (but occasionally shows up in odd places, like Skip Spence's record), the engineers strung up a three-mic spread. They would sum all three channels for a mono release, and split the center channel information left and right for stereo (which is actually more like dual mono).
If you are going to play with three channel, I would suggest trying out the Shel Talmy approach: He used three mics into the space, not across it. Given the instruments and material, you might get some interesting (and useful) results.
