I think part of the interest is because it helps to understand why a particular composition works. You can develop a sense of what works and what doesn't for field use. I can use the Rule of Thirds and similar ideas without grid lines, and this has some similarity.I just recently came across James Cowmans's website on The Art of Composition and have been looking at his videos and articles. I personally don't see how it can be useful to photography, unless it were in setting up a still life or other type of studio shot. It seems that he is only using it after the fact to analyze images. I'd like to see a video where his using it in the field. I don't see how it can be done-- overlaying an armature grid and then connecting diagonal and vertical lines to place compositional elements. Also in his analysis of images, I find that I would choose pretty much the same composition just on an intuitve method of composing.
I'd also like to see some of his own images, but haven't been able to find any. I'd likely be more interested in his approach and teachings if he could support it with a body of his own work. I find it strange that I cant find any of his images online.
I do get the impression he could draw lines and create areas for all but the worst photos. But the idea of connecting elements with diagonals and framing elements in regions of the image makes sense.
I tried to put some of this into use recently. I failed miserably.