What is your target? You want your mixes to still sound good when played over an AM table radio? That used to be the justification for mono compatibility, but I’m not sure what the use case is these days. I do have a table Internet radio type device which is mono, but I don’t worry about the sound quality of that too much, it is basically to play background music, it has pretty limited low and high frequency response, mono compatibility is probably the least of concerns for that style of device.
That is the only mono device I have, I haven’t seen a TV with mono speakers in about a decade and a half, cars have had stereo instead of mono since around 1970, I don’t think any of the personal audio devices are mono, everything uses stereo earbuds now. My point being that “mono compatibility” is in large part a “when I was a kid…” type story that older guys tell you. I mean, have you personally ever thought to yourself “wow, I thought that song sounded better than that, it really doesn’t sound good on that mono .”
Maybe smart speakers. Those little Alexa things (Amazon Echo?) are mono, aren’t they? So I guess if you care how good something sounds on a 3" puck sitting on the table it could still be a concern.
Not generally, no. Mono tracks are for sources that are recorded from a single microphone or single output jack, stereo tracks are for sources which start out with two channels of information for some reason, either a stereo microphone configuration, or electronic instruments which already have panning set, like a drum machine or synthesizer which has panning configured. If you have stereo tracks you generally want them to stay joined so that edits, EQ, reverb sends, etc. stay joined between both sides. If you split a stereo track it just makes twice as much work for you.
Has nothing at all to do with mono compatibility.
There are two aspects to mono compatibility, technical and artistic.
I think technical is the easier of the two to understand, because that is essentially “does the signal change when the L and R channels are added together?” For a source that started as a mono channel and was panned L and R, there are only amplitude differences between the two channels, so when you add the L and R back together, you are back to the original signal. So perfect mono compatibility.
If you add a processor (plugin) before the panner, then again you have a single source signal that is only modified in amplitude to the L and R outputs, so perfect mono compatibility when you add them back together.
If you add a stereo processor after the panner, then you have to understand what that processor does to the phase of the L and R outputs, for example a stereo chorus might shift the phase of the L and R sides either independently, or in opposite directions, so when you add the L and R together you get shifting cancellation. It might sound OK, or it might sound annoying, sometimes you just have to try it and see.
Which gets to the artistic considerations. Human hearing involves processing in the brain, not just the ears, and one of those processes evaluates direction of arrival and creates internal models of sounds to determine where to split attention. For something like a musical instrument with reverberation (either added or recorded at the source), that can mean that what sounds perfectly appropriate when the instrument or voice is at a certain level and direction, with reverb spread across both channels, sounds like too much reverb when the instrument or voice and all of the reverb come from the same direction.
Or the previous example, a stereo chorus might sound nice when spread between L and R, but just makes a shifting comb filter (if you are not familiar, it describes the picture of the frequency response, up and down like the teeth of a comb) when combined into a single channel.
In those cases you just have to decide whether you care that the mono mix doesn’t sound as good, if not then say good enough is good enough and move on, or if you do then figure out how to tweak the stereo mix slightly so the stereo mix still sounds good, and the mono mix sounds better than it did before. That just takes experimenting and experience.