There are a few elite swimmers who do side breathing on butterfly. The advantage is that they don't need to pulse as high to breathe, and since coming up to breathe requires breaking out of your streamlined horizontal body position, it follows that not coming up as much will make you, on the average, more streamlined. But you have to weigh that against the awkwardness, and possibly even the neck strain, produced by side breathing.
As you've noted, both butterfly and breaststroke (unlike freestyle and backstroke) are inherently symmetric strokes, and forward breathing therefore more naturally fits those strokes. There are a number of things that the rules allow that aren't necessarily beneficial to do. If all elite swimmers are doing something a particular way, you probably want to do it that way. If some elite swimmers are doing something one way and some are doing it another way, then it may be worthwhile to try it both ways to see which works best for you.