I'll end up giving a pretty similar argument to what I did in the bounty regarding AI art. After all, there is nothing objective preventing music from saying anything, while our mere human subjective ramblings don't really matter! And trying to give any weight or meaning to our random subjective opinions in the grand scheme of the universe just seems silly.
Naturally there are practical limits to what music can say however, especially if you want to keep it good. Naturally, you can always just make it nothing than an essay essentially, cram more words in than is suitable, and disregard all rules of good music just to focus on getting your point across, though I always stand by that anyone who sacrifices the quality of their art just to send a message, has their priorities severely messed up. The quality of the final piece is what matters, and even if you have something very important to say, no one will listen if there's nothing worth listening to, just making the piece pretentious. And I always thought pretentiousness, at least for me, is one of the biggest turn-offs for pretty much any form of art.
Despite that, it's always interesting to see how musicians manage to really push the limits of what can be said within the limitations of good music that people actually want to listen to, be it with just masterful use of language or lyrics, or the strategic use of the music itself to give a song a certain vibe. I know it may seem obvious, but in music, the lyrics do most of the talking, while the melody is just more of just auxiliary support to reinforce whatever the author is trying to say. Granted, while there is still plenty more experimentation that can be done in that field, pushing the boundaries of what is good and tolerable to the ear to give the song a unique message, however with how long music has existed for, and how many songs are being released daily, we are hitting some limits. But, that experimentation is still going on. After all, that's how we got punk music, and then post-punk from that, from pushing the boundaries of acceptability and seeing what else can be good that can be a tool for delivering the author's intent in a new and creative way while still being good enough musically that it's worth listening to.
While I can't remember any particular moments where I went "wow, I can't believe they managed to say THIS with their music", I'm definitely always surprised by the eloquence of some of my favourite songs and how they are able to put words together in a way I never would've thought of. I write a lot for a living, and I've even written a song before for a project, but there's no better way to make me feel inadequate in my ability as a writer in any scenario than what I see what songwriters can do and how their lyrics often work together.
Even then, what constitutes good or bad is always almost subjective, and in many songs we just have to take the author's word for it they are doing something deeper here, and it isn't just a random collection of thoughts they put together. I do certainly love those songs, where the lyrics just begin to ramble and feel so strange, yet still somehow come together to say something wonderful. It's certainly a hard balance, as one wrong step and you fall into being pretentious, which is again one of the biggest creative sins for me. But for me at least, it works. Take my favourite song of all time for example, a Polish track who's title translates to "Nobody says they're scared of love as beautifully as you", and yes, that is actually the full title. Again, is it just being pretentious and different for the sake of it, did they just want to use the full sentence, or is there something deeper behind it? I don't know, and I will never know unless the author just reveals the intentions, but the weirdness doesn't stop there, as all the lyrics are just so odd. Here's some of my favourites, keep in mind they're translated, so they don't flow as well in English, but honestly they don't even really make sense in Polish either:
Your arms are not crumbling dough
They don't smell like mint paste
I'm in your arms, an insignificant dissonance
A rain of happiness shot over the abyss
or
Before the lightning and the rainbow cross the bridge of sorrows
Before the day flies away on a cloud
Before the peas and the roses kiss over the fence again
Before the dust sweeps the outdoors
No it's not just you, they make very little sense, and just sound like random thoughts the author had. But together, in its own weird way, it does work. The whole song comes together to create something of such emotion to me, that I struggle not to cry whenever I hear it. In these instances, especially if the original intent is not explicitly revealed, either in the song itself or by the musician and only them after the fact (because our own thoughts and theories about the meaning are inherently hollow and pointless) then it just remains a mystery of what is meant on a point-by-point basis here. But together, it comes together to create something with something truly special to say, even if its in ways that are hard to understand. Especially as someone who always struggled communicating with others and knowing what to say, I do find it incredibly comforting, that these strings of random words can come together to create something bigger than itself, and something that does have a grander message in the overall flow, atmosphere, and emotional tone of a song, rather than any single one line.
At the same time, it's also completely ok for music to not say anything at all, for it to just sound good and be pleasant to the ear. There's no music law stating that songs need to have any deeper message or say anything. That idea in itself gives way to a cornucopia of possibilities, be it taking the route of making music in the easy listening genre, or even taking the idea of not taking a point to make a point. To bring up another Polish song, a popular hit from back home is just called "Cash" and the lyrics are all very meta, talking about how that very song is written for money and only money, not to make any point, and to be as hollow as possible.
Overall, no there is no limit to what music can or can't say, because there is nothing physical preventing it from saying literally anything. For me it's as simple as that, it's not a philosophical question, or something that needs to be deeply pondered, it's just a simple fact of life, and by discussing it too much ourselves, we ourselves fall into that trap of just being pretentious, or trying to make a point out of nothing just for the sake of making a point. Be it a story, raw emotions, atmosphere, or anything else, with the right combination of sounds and words it can be done. Naturally only so much can be done whilst remaining of the confines of what most people would call "good" music, and you can make the world's best, most thought-provoking point, or you could even reveal the mysteries to life itself, cures to the world's worst diseases, and more, but it doesn't matter if no one will listen if the song itself is bad, and whatever you have to say will just bounce of a wall.