Dave, great topic!
I can think of a lot of reasons to put up multiple mics...and not just because I have dozens of mics that I would otherwise never use...
Placed close to a source, different mics can capture radically different sounds. Having some options at mix time can be a blessing, so long as you don't over do it.
Your example of putting up a mic in the room is a really great idea, too. Natural ambience sounds really different than digital reverb.
I remember tracking drums with all sorts of crazy mic combinations over the years -- a PZM taped to a Manhasset music stand as a third drum "overhead," omni dynamics shoved up against the snare drum shell, a condenser out in the stairwell (hoping for some Bonham reverb), a Fig-8 ribbon sideways at the front of the kit (with the kit in the null so the mic only hears the room), etc. Lots of times those experiments were not worth listening to, but the experiments were definitely worth trying.
I'd be less inclined to do anything too offbeat now, but I would definitely put up a room mic for most instrumental sources. And I'd put a couple very different mics on a guitar cab, e.g. a ribbon and a condenser, or a dark dynamic next to an SM57, etc.