Are there any circumstances in which composition isn't necessary and if so, what are they?
I don't think there is any image that couldn't or wouldn't be better if it were strongly composed. That said, there are a number of images in which other factors are more important than careful use of edges, leading lines, interesting use of negative space and so on.
The expression on a naughty child might well far outweigh any benefits from careful composition. In some images, colour is the overwhelmingly important element of the image and everything else comes secondary. A black and white image may have some wonderful tones which don't form any logical pattern or sequence yet are sufficiently strong to make composition of secondary importance.
Whether any of the above images would be even better if in addition to all its strengths it were strongly composed too is uncertain. For sure if you have two images of equal merit in other ways, then I'd select the strongly composed one every time. I can't think of any examples in which a strong composition interfered with the enjoyment of other aspects of an image - though I'd be interested in your thoughts on this. Often though, the circumstances are such that the great colour only comes without composition and if I insisted on strong composition, then the image wouldn't be. In capturing kids, often it's all you can do to catch the moment, never mind the composition, but Cartier Bresson sure managed it - by working on the composition first then waiting for the subject to place them selves just so - a matter of skill and perseverance and organization.