It really depends on why you're creating art in the first place. Sometimes you don't create to give a message. Sometimes you create for the joy and sake of creating, and in that space you'll find a lot of, "find your own meaning" type of thinking.

I'm a writer. I work as what's called a "direct conversion copywriter." Meaning, I write things to try to get people to take a particular action, like signing up for a newsletter, donating to a cause, or buying a product. Writing that kind of material is different than writing a piece of material that's just meant to convey a message. I think that difference gets lost on a lot of people who are creating things to try to inspire other people to action. You can absolutely amp someone up and then they have nowhere to go with it because you didn't point them in any direction. But sometimes that's not the point. Sometimes the point is just to get amped up, sometimes it's to convince, sometimes it's just to kick back and engage in some escapism for awhile with something you enjoy.

So, to answer your questions more specifically...

But if we take an anything goes approach to what lyrics mean, or what artwork means, then really, one could come away with anything. Why not just use a random word generator and find meaning in that instead?

That's comparing apples with oranges. How a person takes a piece of art should be in the context in which the artist created it.

Isn't there some value in communicating something solid?

Yes, but not every artist is trying to communicate something solid. Sometimes we're just creating for the pleasure of engaging in our craft.

Isn't there some joy in being able to connect with what the creator of the work meant, and resonate with others about that meaning?

There is, assuming there is meaning there to begin with.