I get the feeling that people do not understand the phase cancellation problem when summing stereo audio signals to mono, though it's been explained in many ways.

I'll try again: the problem only occurs when the same sound occurs with itself but out of phase. A sound wave has an up and down cycle... now if you take two of the same sound and they occur simultaneously - nothing happens, but if one of those sounds is delayed by an incredibly small amount, then the "up" cycle of one wave will occur at the "down" cycle of itself, thus cancelling each other out. This is phase cancellation.

The problem occurs for keyboardists when you sum the left and right signals of a stereo signal like a piano into mono, and because of many possible factors then some of the tones wind up cancelling each other. The result is a "phasey" tone that seems to be missing some of it's mid-range (although all of the frequencies can be affected to some degree, while other frequenciess may not be affected at all, depending on which up & down cycles collide and when). The exact tones that are affected vary widely depending on keyboard and sound system.

You can do a search for "audio phase cancellation" and get much more detailed explanations, theories and diagrams.