Audio compression with STFT
I see two big drawbacks to your method:


The image you posted is not the STFT, but its magnitude. The difference between the magnitude of adjacent STFT frames is small; so for your scheme to work you would have to store the magnitude and phase separately. But then, there would be no compression at all on the phase data that would still represent 50% of the data and would be required for reconstructing the signal. Try plotting the phase (angle) of the STFT to see how ugly it is.
Assuming the deltas are encoded using variable-length integers or Golomb codes (I assume that's the idea behind it...), your method would compress large and temporally stable values in the spectrum (the red "lines" on the spectrogram image). It's obvious that these represent only a small fraction of the values. There would be no gain for the background "noise" which amounts for a very large portion of the spectrogram magnitude data.


A much more efficient way of getting rid of these stable/predictable peaks in the spectrogram is to whiten the signal and code the residual+the filter coefficients. This is (among other things) the principle of the FLAC lossless codec.