> So you would think that it would make sense to break the signal down into stuff with frequency and time. Some kind of wavelet probably. Maybe something that very accurately models what a human hears.

Interestingly wavelet based compression went nowhere because although they have nice mathematical properties, when applied in a lossy compression scheme, they did not fit well with how humans perceive detail/quality, both in terms of psychoaccoustics and psychovisuals, i.e. PSNR vs subjective quality diverged more than with other systems. Not surprisingly none of the state of the art lossy compression algorithms use wavelets.