sofdavarhakolnishma-
First of all most frum, ehrliche people who hear a song that is actually classified ‘rock’ or ‘jazz’ would probably think it is either 1) very nice or 2) incomprehensible, just as classical music is not understood by many people who are just used to simple jingles. The styles you probably really mean are heavy metal, hip-hop, and the like.
That’s just semantics. But you are wrong anyway. I am going to guess that you aren’t Syrian. Have you ever been to the kosel and heard their tune for slichos? To a regular Ashkenazic Jew it sounds really funny, the tune sounds like a bunch of kids singing a nursery rhyme. Yet they are so inspired by the tune, as you probably get inspired by koh echsof. You hear the tunes the Arabs play over the loudspeakers in their mosques, and they sound dull and boring. Yet they are inspired by that in the very same way that we are inspired by u’nisaneh tokef. And it isn’t just the Arabs; the music of Jews from Arabic regions sounds the same.
My point is, who gave you the right to judge an American singer composing tunes for an American crowd, by saying the songs don’t match the words? They don’t match the words TO YOU, because YOU are used to the music of the society and community YOU grew up in. Of course the American-style Shema Koleinu won’t inspire you and the American-style Al Naharos Bavel won’t make you cry, because you were brought up with a different kind of music. But to someone more American-oriented, the songs are more-often-than-not on target and in line with what would seem to be the original intent.
There is no good or bad style of music, and I challenge anyone to find me a makor in halacha (shas/poskim) that proves otherwise.