Composers definitely have intentions when writing a piece and, if they're any good at all, some of those thoughts and feelings are conveyed to the listener. However, I think the issue is less about what the music was designed to do and more about people's general perception of music. Here's two things that I've observed and believe to be true usually:

1. Repetitive music is harder to ignore.

2. Music with words in your language is harder to ignore.

If I put on music to concentrate on something, it would need to be music that can be temporarily ignored and then refocused on when I finish the micro-task at hand. Rinse and repeat and those moments eventually build up to your finished essay or math homework. I'd say this is why concentration music, for me, is almost always classical or jazz. Don't misunderstand me, I have a deep affection for both of those genres and have been moved deeply by certain tunes from both of them. But that doesn't stop me from admitting that often they work equally well as background.