I definitely disagree with some of Babbitt's more radical views on music, specifically the belief that music should be composed for the sake of academia. Now, with that opinion aside, I really do admire and enjoy Milton Babbitt's music. In fact, one of my teachers studied with him at Princeton. However, not all contemporary aesthetes (associated with the composition of atonal music) share the same views as Babbitt. Many composers, both living in dead, throughout the 20th and 21st centuries (including Arnold Schoenberg) have espoused the viewpoint that (free) atonality is the natural continuation of the romantic style of music, but eventually the need for a set procedural structure pushed composers of atonal music to use serialism. Some composers abandoned the triadic system all together, but others, such as Alban Berg and Paul Hindemith integrated triadic harmonies into both free and serialized atonality. Have you ever heard the Berg Violin Concerto? Listen to the last movement- a beautiful example of serialized, triadic atonality. I think you'd like it, antiatonality.
On this concept of "newness," I think we all can agree on one thing- that it is OK to draw upon earlier forms for inspiration, or guidance and perhaps even utilize them in a way which integrates elements of music of our age, with music of the past. Now, there is LOTS of "new" tonal music being composed right now, but what makes it new is its utilization of tonality, just as Alban Berg's use of serlialism is new, or innovative.