I don't think it's that straightforward. Loanwords happen overwhelmingly with vocabulary, and not grammar. While this is obvious, the implications are thus: the closer to script of the origin language to the borrower language, it is exceedingly easy to take the target word wholesale. Since the grammar is relatively stable, you can easily make the case that the loanword, whose origin is language X, is no longer language X, but language Y, the borrower's native language.

That is, words like "tempo," "crescendo," and "forte" are Italian in origin, but who's going to say, no, they're not English? They're native enough.

Now, let's take a discipline with non-English terms. Take Go for example. There are many terms in Go that are shared between Chinese, Japanese, and Korean schools. They can be written similarly in hanzi/kanji/hanja, with two catches: 1., the same characters are read differently in different places; 2., Westerners, using exclusively the Latin alphabet for their native needs, cannot read the hieroglyphs.

The result? What term should English speakers use? Pick one! Which one? Whichever! For Go, the Western world picked Japanese. You have ko, moku, seki... So which was the common language? There are now two answers. First, there was a common script, which was Chinese characters. Second, there was a commonized pronunciation, which came from Romanized Japanese.

It's not a "so happens to be" thing. It's a speed and scale of adoption thing, and in this way it is a "majority wins" game. And here, the winner is the Latin alphabet. To come around, I would suspect there are few disciplines that do not turn into a Latin-alphabet-standardized-, and in effect, English-, field.

The terminology used in music composition are in Italian, but are the research papers and discussions written in Italian?