But I wonder if there isn't a gem in there somewhere. The essential expressive characteristics of a person's voice change much more slowly than the frame rate of any codec, and predictive coding alone doesn't cover all of the possibilities. There are also not that many unique human voices in the world. If you had several thousand people read a given passage and asked me to listen to them and tell me which voice belongs to a close friend or relative, I doubt I could do it.
So, if a codec could adequately pigeonhole the speaker's inflection, accent, timbre, pacing, and other characteristics and send that information only once per transmission, or whenever it actually changes, then a text-to-speech solution with appropriate metadata describing how to 'render' the voice might work really well.
Put another way, I doubt the nerves between your brain and your larynx carry anything close to 1.6 kbps of bandwidth. Near-optimal compression might be achieved by modeling the larynx accurately alongside the actual nerve signals that drive it, rather than by trying to represent both with a traditional frame-based predictive model.