Oh wow. Right. "Easily be divided" into three broad categories? I find your divisions rather ridiculous, specifically the first one. I mean, isolating music that (and I quote):
Since, you know, exploring something so rare and obscure as EMOTIONS (in art, no less!) requires a specific division. Seriously? So you mean to tell me that music in your other two categories do NOT "express and explore" emotional states? Maybe you think that's not a "primary" focus, but then again how do you even know that? How do you even go about telling if that's the case?
But this doesn't mean the other two divisions make any more sense. So you figure music "connected to dance" needs its own category, when in reality the only parameter you seem to be looking at is the prominence of rhythm. I don't see the point, again, since I don't see how this is any different than giving incidental music its own category (at least according to your own reasoning.) Wait, that would actually make more sense than your suggestion, nevermind. Oh yeah, by the way? Every composer that has ever written a minuet or any kind of dance piece would fit here according to you, so that's the VAST MAJORITY of classical composers. Or do you mean composers who only write dance-type music? Since the examples you gave make no sense, listing minimalism as if that was inherently connected to dance (which is arguably true in some cases like Steve Reich's Drumming! Oh wait I wasn't supposed to mention specific works, right? Is that how this works?) Glass also wrote a violin concerto, should we also put him in all three categories then??
The third is just a joke. I don't know, you wanted to equate ritual behaviors with concert-situation? Is that the parallel you wanted to draw? So it's spiritual since, uh, you can't drink beer, dance and scream during a performance of Beethoven? Also, you say ineffable, but as far as I could tell people write music because music is the proper medium for those ideas that cannot be expressed in any other medium that isn't music. I mean, I don't see anyone saying "Man, this 4 voice fugue in baroque style I'm writing would work out so much better as a stage play instead!" When music is insufficient on its own, you can add things to it, such as text and scenery (operas for example) or perhaps it needs to complement something (incidental music.) There's no 1-1 translation of music to any other art form, so even bringing this up is a waste of time.
Honestly I'd prefer something more complex but that actually makes sense if I'm categorizing music. In fact, music is so diverse that ANY method of categorization is a disaster if it tries to be more general than fact-based things, such as music that comes from a specific geographical region, or time period, etc. Style and aesthetic categorization are always, therefore, coupled with factual information to actually place it somewhere objective. Even then it's a problem, just like throwing terminology around is--oops getting ahead of myself there.
Ah. Seriously? Is that what the kids are doing these days, huh? I'm sorry, but if you're just going to list ways in which artistic creation can be justified according to the ways in which the material itself is manipulated in relation to its cultural and historical context, we can be here all day. You missed a bunch too, like people who write music just to spite your type of categorization schemes or people who create music without needing any of the motives you listed, really.
What's kind of hilarious about your analysis there is that, taking into account only a single composer's output, you can find all those categories and probably much much more in terms of artistic motivation. So what's the point, really? Categorizing by piece if we happen to even know what the motivations were? What if we don't? What if the composer didn't ever say? What if it's an anonymous piece?
Next you'll tell me you can infer these things from the musical material on its own, at which point I would love to see the amazing mental gymnastics you'd need to pull off to justify such a ridiculous proposition.
Protip: Don't.