Most musical instruments have a Mono output and the cables were used to are Mono TRS “Tip Ring Sleeve”. Stereo cables such as those on our headphones are TRRS (2 rings for 2 channels), and if you have one with a mic, well you probably guessed by now: TRRRS
There are some pedals that split your signal so you can process 2 channels with different effects and then give you the option to combine them back into mono for one signal (this is essentially what a blend knob does!when in middle position) or keep it stereo if you are sending it to 2 different locations.
As far as audio quality, I can’t answer that, but I doubt it makes much of a real difference considering what all these modern pedals do, and how many musicians use them.
I do remember that when connecting Mono Signal into stereo inputs, the Left channel was the dedicated mono channel, not sure if this still matters.