I think it's true generally that the best poems aren't the ones that make the best songs, and the other way round. Yeats wrote a lot of poems which as poems have much more power than the Sally Gardens, but they probably wouldn't make anywhere near as good songs. I doubt if many people would rank Kipling as high as Gerald Manley Hopkins, as a poet, but when it comes to verse that makes good songs he's pretty good.
There are exceptions. One that I'd put in that category among modern songs would be Dave Goulder's The January Man (and others by him as well). And that's an example of a song that doesn't need to have an instrumental accompaniment, and in fact is likely to lose by having one imposed on it.