Stereo is not just two channels - although that is required - just because you have a left and a right channel does not make a signal stereo.
There is a component of how the two channels interact with one another. Not to make it over complicated, but true Stereo is where you have the illusion of the sound not originating necessarily where the speaker is.

In other words, in true stereo, you can create the illusion of someone walking across the room in front of you. When you sit in an equilateral triangle in front of a pair of speakers being fed a stereo sound source, by adding electrical resistance to one channel this makes it easy for the signal to flow to the other channel, as you decrease that resistance the signal will start to travel to both speakers and the source will seem to “move” toward the center, as you increase resistance now to the opposite channel, the sound will find its way to the least resistance and the illusion that the sound moved across to the other side is complete.

You can have the audio of the footsteps march from left to right in front of the listener, and back again... by simply “panning” the signal.

If you send an equal amount of signal to both the left and right speakers, the illusion of movement will be lost. So stereo is the interaction of the left and right channel, such that you can place instruments in the imaginary horizontal panorama between the speakers. You can place the 6-string Rhythm guitar more towards the left of the stage, and the 12-string Guitar more towards the right side...

Once you record as mono the possibility of this illusion I’ve been describing is GONE. You’ll hear the footsteps but you will get no sense of them traveling any where. If they get louder your ear/brain might think they are getting closer. But you will have no illusion of them passing by in front of you. Is that a clear enough picture? With stereo I can not only make the person sound as if they are getting closer but I can have them walk by the listener and disappear out the opposite side of the room.

When you plug a cable into just the L/MONO output, yes, both left and right channel are intelligently merged - but instead of cancelling out, they are phase coherently merged so that the sound is MONO and at least it does not degrade completely (or what is called “phase cancel”... All the magical left/right movement is gone. It’s irreversibly mono. But at least it doesn’t phase cancel. And no you cannot get it back.

Is that clear?

Stereo is more than just two channels - it’s two channels where you have the freedom to “place” signal across the imaginary left-right panorama established by the placement of the speakers. The Pan Pot (panorama potentiometer) is the Control that determines how much Signal is sent to the left or right channel for each of your systems Parts/Channels. If you want the bass sound in the middle, you would set the Pan Pot on that channel to C (center)... this ensures an equal amount of signal arrives in both the left and right channel. The Pan Pot is a dial that increases resistance in one channel sending more if it to the opposite side... causing the ear/brain to be fooled into thinking the signal source has been moved.

Thank you for the response, Bad Mister. It was very informative and educative.
So, just to check if I got it right, do you imply that if I were to just sum the left and right channels of my (true) stereo recordings to mono in my DAW, phase cancellation would occur and the result would be inferior/different to mono recordings of just the L/Mono output (because when only the L/Mono output is used the channels are "phase coherently merged")?
In that case, I guess I'll go with 2 set of recordings in the pre-production stage - a stereo one and an L/Mono one, until I determine what works best for the song.