I agree. Although to me the proverbal chromatic is a sequence of notes that moves in step-wise fashion, like Flight of the bumblebee. And composing music chromatically implies the thought of doing so without a tonal center in mind, although later one can easily be sensed, like flight of the bumblebee.

I have tried to write music using serialism and have only been able to achieve it through systematically plotting out all twelve notes until it seems somewhat musical. It's possible but in hopes of breaking away from the ties of tonality, it places far more boundaries on music then say the major scale does. One the music in my head just doesn't play in such a way, and second I believe once the melody has started all the composer can do it ride it out. So saying I can't do this until I play all these notes doesn't make sense.

Though I do believe it is possible to compose using the chromatic scale. Like every other scale it too has a distinctive sound. Very fluid as it inquires the movement to ascend, descend, or zig-zag in half steps. But ultimately if you add a harmony, a tonality will be established and the view you have on chromatics definitely makes sense.