If you think you absolutely need to stereo process a stereo instrument.
Ha! I don't think I absolutely
need to process a stereo instrument in stereo, although I must admit, for me, it does seem to make some modicum of sense, especially with keyboards like the Wavestate, Mini-Freak, and softsynths like Heavyocity, Spitfire, and ProjectSAM which have entirely different (or very close to it) program material on the left output vs the right. I'm probably thinking more in terms of audio 101 than my thinking of personal absolute needs.
You have however largely piqued my curiosity.

In what scenario, like the one we're discussing, would it make sense (as opposed to me thinking I absolutely need something) to collapse a massive broad stereo field down to mono? I must admit I can't, off the top of my head, think of any.
Yes I've tried left and right Monitor sends but across a large session, it's not particularly an elegant solution. It would seem to me, and it's only me, that it wouldn't take much to design a stereo-out TRS solution for each monitor send. Internally that is in fact what the on-board FX section does, A sub-send and return would be just biblically inefficient, at least for me.
I was using ping-pong delay merely anecdotally. Just something that folks could easily wrap their heads around the scenario that provided a wide stereo field. I must admit I don't think I've ever, in 25 years of post-production, used a ping-pong delay.
YMMV
