Certainly *diegetic* sounds in FPS or RPGs or WoW or whatever often provide useful cues in addition to enhancing that "immersive" experience, and in puzzle games the sounds are content-ful. I would distinguish both cases from background music, but I do acknowledge that "background music" can in fact track with the game action, as in different music for battle vs exploration as a simple example. I agree that game designers can use music very intentionally, and i'm missing out on that when i turn the music off.
I would never advocate anybody adopt my approach, and I totally understand that it would harm the gaming experience for some. I just really don't like the majority of music I find in games. Perhaps also coloring my experience is the fact that I play very few high-end games.