What are best practices to compute an audio spectrogram?
I think, perhaps, that the statement should be reversed: that a lot of implementations "just" use the square magnitude. This is because the DFT of a real-valued signal is typically complex, so that the square magnitude is just the product of complex conjugates, e.g.:


  X*(f) &middot; X(f)


This requires less computation than the magnitude, which would follow the same algorithm, but with a subsequent square-root. 

The square magnitude of a DFT is formally known as the Power Spectrum.