Hmm, convolution is perfectly good operation to run on wave forms as well. In fact the wikipedia article (https://en.wikipedia.org/wiki/Convolution) shows the operation on functions which would correspond to time-domain wave forms. What is the point of converting everything to pictures and then using 2D convolutions when that step could have been skipped entirely?

Converting to pictures is unnecessary. It makes the processing harder. The pooling should just happen on segments of the wave form instead of the fourier transform (frequency-domain) picture spectrograms.