Answer: That is a very thoughtful question.
While I'd love to say I have the final answer, all I or anyone else can really offer with something like this is a theory:
I like to think that every piece of music is a little like a new language that we learn as we hear it. Time just keeps on rolling by, and it's hard to grasp the whole of a series of events in time unless parts of it repeat. I think repetition, which is a very old practice in music, is there because there is a different kind of delight to be found when you go through something for the second time: now you've started to "get" it, as you say, and you hear it in a different way.
And this effect endures, I think, even in pieces we have played or heard many times.
After presenting his "Paris" symphony in that city, the young Mozart wrote home to exult to his father about a theme in the first movement that he was certain the audience would love. And, he related: sure enough, when the orchestra reached that part the audience cheered and clapped! And when that tune came back in the ritornello (the repeat) the audience cheered and clapped even more! (That's during the music! Think of this when someone admonishes an audience for clapping between movements of a Mozart symphony).
In an age when music could only be heard "live" repeats perhaps had added significance, but even now we seem to appreciate them.
The repeat is especially important in dance music, and there one can imagine it having a practical value: the repeat sections allow the dancer to clearly understand the divisions in the music. Even in non-dance music, the repeat of former material helps to give the music understandable form.
In the Sonata form, the basis of most traditional first movements of Symphonies, there is another kind of repeat. The first section normally modulates to the dominant key, repeats exactly, and then there is a "development" section that plays with the music of the first section and visits sometimes a number of keys. Finally the music of the first section returns - but now it's like the return of an old friend. The old friend has altered somewhat after the experience of the development section, however, and no longer modulates to the dominant in its second part.
The variation form is also based on repeat, but in the variation every "repeat" is different - still recognizable, but different - and at the very end the original theme returns again just as it was in the beginning, and again there is a certain satisfaction in that roundness.
Some composers might recycle material into a new work for pay, but I don't think that the repeats were there to add to their fees - after all, a repeat mark doesn't really add any notes to the score. The repeats were what the customers expected and needed in order to make sense of the music.
In the realm of popular music you hear very few songs that are "through-composed" - without verses and choruses. Generally we find some pleasure in repeating a chorus and hearing a verse with new lyrics. There are a few exceptions to this, like Roy Orbison's "In Dreams," which builds and builds and doesn't repeat a section at all. But that just reminds you of how unusual is that approach.
