Poking around various web sites for these "rules" is always an exercise in hilarity. You'll find examples of "rule of thirds" with lines carefully drawn through the subject, and nowhere near a one-third line, you'll find ludicrously squashed golden spirals. You'll find golden triangles proudly drawn on top of examples images that bear no graphical relation to the drawn figure whatsoever.
Why do I care about rules of composition, today? I'm interested in whether "good photographs" tend to use these things or not. I'm also interested in, when we examine a "good photograph" for rule compliance, to what extent are we doing ex post facto fitting of patterns to reality, and to what extent the photograph actually deployed some rule or another.
There are two ways to approach this, or perhaps two ends to a spectrum of ways. One can say that in order to be judged "compliant with a rule" the main subject and other elements must be exactly placed according to the rule. One can also allow a moderate degree of latitude, and say that the main subject and other elements must only be placed approximately in the right places to be deemed "following such and such a rule".
One gets in to trouble in both directions.
Rules of composition tend to be very crop-sensitive. If you change the crop, the designated locations for subjects and so on move around, sometimes quite dramatically. Surely a great photograph remains great if you shave off 10% on one edge or another? Or at any rate many of them do. If you demand extreme precision in placements, you will find almost no good photographs that follow the rule -- although you will certainly find many postcards and calendars that have the bear's nose, or the boat, or the top of the waterfall slavishly placed exactly on the intersection of two 1/3 lines. These photographs would in general be improved by any crop at all, the more complete the better.
If you permit rough compliance, then many more good pictures will be found to be in compliance with some rule or another. If you have enough rules, you can find one for any occasion. This image:
Why not just say "stick the things that matter in the frame, not at the edges and not in the center, unless there's a good reason for it"? Why not talk about balance of visual masses, eye leading, and so on?
It is absolutely the case that every rule of composition can produce a pleasing balance of forms within the frame. To codify these things as rules, however, is to place the cart well before the horse. We might as well say that to produce an appealing cheese, you should wrap whatever it is you have handy, some milk solids, old clothes, a dead cat, perhaps some mud or a set of house keys to a house you no longer own, in a layer of suitable wax and place the result it in a cave for a few months.
This is, after all, how many excellent cheeses are made. So it works, some of the time.