That seems a rather rigid stance. Those same composers may have studied theory, incorporated its elements, and invented new variations that gained adoption which then become theory, right? It feels a bit like language in that sense.
To use your analogy: composers are inventing music in the same way that normal speakers invent language. I don't think I'd describe new variations on language as "inventing linguistics," though, as linguistics is the in-depth study of language (and as such, "inventing linguistics" is something done by linguists, not by language speakers). But language is not linguistics, in the same way that music is not music theory.
Well, that's a contradiction with: "the research that professional music theorists do is designing theories to describe music we see and hear in the real world".
Given the later, it's actually "people writing music" who create new music theory. Music theorists merely takes notes and write it down (formalize it, descriptively).
>I don't think I'd describe new variations on language as "inventing linguistics," though, as linguistics is the in-depth study of language (and as such, "inventing linguistics" is something done by linguists, not by language speakers).
Well, linguistics is not inventing, but describing what language speakers do in a formal language. We could say they "invent linguistics", but that would be like saying a secretary "invents the typed note" someone dictates to them.
So music theorists might "invent music theory for X", but composers invented X (e.g. modal interchange).