Are these notations really just for obscure atonal, chromatic, twelve-tone music, and not suited for the tonal diatonic music that everyone likes?
No, notations with a chromatic staff actually represent the interval relationships that are fundamental to diatonic music much more accurately than traditional notation does (see Intro: Interval relationships and Intervals Tutorial). So we think this approach offers advantages for tonal diatonic music (or any kind of music).
