Modal mixture is simply one lens through which to understand why certain chords sound good in certain contexts, but it's by no means the only way to look at it.
Music theory seeks to describe why certain musical devices sound good, to try and write music that sounds good by applying some set of rules is getting it completely backwards.
Don't get me wrong, modal mixture is a perfectly valid way to understand a lot of moments of pieces, but it is that; a way to understand why some things sounds good, not a ruled about which chords you "can" use in a certain key, and in some situations it's a useful way to look at it, and in other situations it isn't. What it certainly isn't is a rule for what chords you "can" use in a song.
For example, in common the chord progression:
| C | C | F | Fm6 | C
It's useful to explain borrowing the Fm6 as a "borrowed chord" from the parallel minor, and it sort of helps us why it has the sound of "getting sadder" more or less from the F to the F minor.
On the other hand, you can also look at the voice leading A>Ab>G and say "the F minor sounds good because it is a chromatic passing tone between F and F minor".
And guess what, in this case, they're both right!
On the other hand, if I changed the chord progression slightly:
| C | C7 | F | Fm6 | C
Now, why does that C7 sound good? I could say "it's modal mixture, it's a borrowing from the parallel mixolydian" and I suppose, technically, on paper, it's not wrong. All the notes in that chord are contained in the mixolydian scale, but it doesn't really help us understand what's going on at all.
A better explanation would be that C7 is the V7 chord of F, and so the C7 helps us lead into the F chord nicely and makes the movement a bit stronger, and it prepares us for the chord change that's about to happen. You could consider it a secondary dominant.
And then you take a chord progression like
| C | Am | D7 | G7 | C |
In this example, it has nothing to do with modal mixture. I suppose technically you chord example the D7 as a "lydian borrowing" but really what you have is a classic II V7 I. We use D7 instead of Dm because it prepares the G7 nicely.
Take the famous jazz progression:
| C | A7 | D7 | G7 | C
This one uses the same function as above, but one more level; the A7 is the V of the D7, the D7 is the V7 of the G7, and then you're back home. And this isn't some sort of bizarre esoteric weird sounding "experimental chromatic" progression, it's used everywhere; it's the chords for the chorus of "Oooh, I wanna be like youuu, I wanna walk like you, talk like you..." right?
The point is that there are many different musical devices that help us understand why certain things sound good. In some music, diatonic harmony and modal mixture is a useful thing to think about. In some music, other functional devices are more important (I've just given you 2 really common ones, secondary dominants and voice leading). In other music a bunch of other things are going on. Hell, in some music even the concept of "melody with chords" isn't really the best way to look at it, you have to look at the movement of individual independent voices, or microtonal inflections, or something else entirely!
In the comments you said:
then this site wouldn't be needed. The only guidance would be "meh, just use the chromatic scale to make music!"
In a sense, that's true, to the extent that every note in the chromatic scale, and pretty much every combination of notes (or at least a large large number of them) can be used in a certain key and sound good, given the right context. But that doesn't mean "abandon all theory, just stab at the chromatic scale at random because everything's fine", but it does mean "there is no enforcing a fixed set of allowed and disallowed notes or chords in a key." and it does mean "experiment freely, and see if you find something that sounds good, look in detail at the songs you like and notice what's going on in them, and see if you can understand why things that you like sound good.", and it does mean "learn to play a lot of music so that you can come across new musical features (e.g. chord progressions) and add them to your vocabulary"
If you come across something in a song that you like but you have no idea why it should sound good because it doesn't fit with any of your existing knowledge of harmonic analysis, or you stumble across something while playing around at the piano but you don't understand why it works, but nevertheless you like it, then that's a great time to try and figure out what's going on, and build your knowledge (and that's one of the many things this site is great for).
Also, do be really wary of youtube theorists who look at everything in terms of "scales" and "modes". I'm not saying there's not some valuable material there (there is), but often it's significantly overdone because scales and modes are a nice neat general system logical with clear labels and names, and they can be shoehorned nicely into the youtube infotainment video format.
As a final tip, because I do really want to be helpful and not just seem over critical.
If you're noodling at the piano or whatever polyphonic instrument you're playing with, and you want to see if you can find some more "out there" chords that are a little more non-conventional and spice things up, try making chromatic alterations to whatever you're already playing (changing 1 note in a chord by a semitone in either direction and just seeing what comes out), you might stumble on something you like, and then later you'll probably find out why it works. It's one technique among many that can help you to add a bit more non diatonic notes into your music if that's what you're looking for!
