A big reason against FFT is latency - for good resolution at low frquencies you need a big FFT, so it takes longer to buffer that many samples before you can FF

A big reason against FFT is latency - for good resolution at low frquencies you need a big FFT, so it takes longer to buffer that many samples before you can FFT them. Also a lot of the processes we want to apply to audio have much more efficient methods available than FFT or convolution such as IIR filters - which also have no latency apart from whatever phase shift they introduce. Or if the process is time varying or has embedded non-linearities then it lends itself to sample-by-sample processing and not block based like FFT and (efficient) convolution.