Even if the only person who can predict the melodies, progressions, and rhythm is the composer, doesn't that inherently make the composition less random than completely unpredictable and truly random TV noise?
In historical serial music there is certainly a leftover of human interaction with the compositional rule system, so in practice it resembles more to a chaotic attractor than complete noise, i agree. The core conceptual idea of serial music is however the inevitable disembodyment of historic human music into pure structural sound patterns beyond history and beyond (historic) emotions.
Even if they're purely structural, how does that make them non-rhythmic or non-melodic?