A spectrogram has time on one axis and frequency on the other, so the ultimate result is a multiplication in one dimension and a convolution in the other. It can be used to show things like when a note starts and stops in a piece of music, which is difficult in either purely-time or purely-frequency space.

Also, it’s computationally intractable to individually train 2^N weights. What a CNN does instead is train a convolution kernel which is passed over the whole domain to produce the input for the next layer; by operating in frequency space, it’s considering the basis functions e^{j omega +- epsilon} instead of delta(x +- epsilon)