Tolkien himself has never given an explanation of why there were so many songs in his works.
This article, entitled "Why Does J.R.R. Tolkien Put So Many Songs Into his Books?", says basically that there's no canon answer before going on to consider a different question.
But we know that Tolkien enjoyed poetry and writing poetry in general (see e.g. the collection The Adventures of Tom Bombadil), and was a fan of classical poetry such as the Iliad and Odyssey and Norse sagas, the latter of which at least were a great influence on his writing. All of which would tend to make him want to include lots of poetry in his books, without needing to justify it in terms of in-universe theology.