Why do we sing accompanied?

How come lectures don't have guitars strumming along?

When a poem is recited, must it have instruments, too?

And when I am speaking, I am communicating with language in a certain intonational pattern. Does that require instruments?

My point is that singing (of actual language, not vocables or scat) is an extension of linguistic expression. It could even be thought of as one mode or register of speech, albeit one that is intoned more dramatically. "Song" (i.e. versus "lecture", etc) tends to be distinguished by the form of the text: verse.

Poetry is (often) verse. It is not surprising that in many poetic traditions, a "recitation" of poetry means doing what most would call singing. Take India as an example, where most poetry is customarily sung as a matter of course. I'm sure this was the case at cetain stages/places with English verse, too (others could say more).

Also note that in the Indian system (as lots of others), a "song" is first and foremost categorized as falling under "literature" -- in the broad sense that includes "verse" -- NOT "music" per se.

So I suggest we think of singing as a textual expression, heightened (for whatever motivation) by more distinct rhythm and pitch contours -- that is, RATHER THAN music minus instruments!

In many societies, there is a clear distinction between what it means to sing and what it means to play an instrument. For example, in a music culture with which I am very familiar, northwest India, women don't customarily play instruments. It is not their gender role to do so. That would be performing "music," which is an act fraught with many conditions and assumptions. However, women do sing-- many many more traditional songs than men in fact. That is "singing." You find a similar split between "amateurs" and "professionals"; instruments are tools, not to be used by amateurs, while on the other hand everybody can and does sing. There are also sacred vs. profane distinctions, mostly related to that fact that, again, instruments spell "music" (which may be considered inappropriate in many religious contexts) while singing (unaccompanied) is innocuous.

Quranic chant, the Islamic call to prayer, etc, mentioned by the OP, are famous examples of non-music -- despite that cultural outsiders may perceive them as "music". Rather, the text is being intoned or chanted. There are many reasons to do that, least of which (as with many ballads, too) the melody aids in memorization of long texts.

Accompanied singing often has a different style and form from unaccompanied -- it's not just that you subtract instruments and you get "unaccompanied singing"! For instance, most songs that are "meant to be" (*debatably) sung unaccompanied will clearly show their rhythm in the melody, while other kinds of songs have melodies that complement instrumental parts (and would thus sound silly unaccompanied). The majority of pop songs today, for example, seem to wait until after the first beat of the measure before you hear singing start; you hear the instruments hit the downbeat first. This is probably the legacy of genres like jazz, r 'n' b, rock n roll, etc., that had that sort of rhythmic sensibility, meant to be played with drums or other rhythmic instruments and perhaps danced to.

Just listen to what we often code as a (English lang.) "folk" song versus a pop song and you'll see that the "folk" song carries its own meter. IMHO, a lot of those songs don't need any instrumental accompaniment, and it is partly there because people had developed this sort of fetish of carrying an instrument...something iconic about it. I remember seeing Pete Seeger interacting on his old TV show with an African-American woman singer (I forget who)...She was singing folk songs that obviously took no accompaniment, but there was Pete, nosing around on the banjo.   Again, only my biased suspicion, but I think it became a "thing" for revival-folkies to carry instruments as a sheriff carries a gun...and it is sometimes hard for people to break away from that and consider WHY they are singing, WHAT it really means to be communicating in that mode, and whether they are a "musical entertainer" or someone who merely sings...just because it's what humans do.