Mostly because of frequency resolution and latency. The Mel Spectrogram is just a Short Term Fourier Transform with some remapping of the frequency axis.
The resolution the Discrete Fourier Transform (DFT) is a function of the transform length. The more resolution you need, the longer the time domain window needs to be.
If you want to build a guitar tuner with accuracy of 1 cent for the low E string, you would need a resolution of around 0.05Hz. This would require a DFT that's 20 seconds long. That's simply not practical. There are ways of interpolating with shorter time domain windows, but it's fairly expensive in terms of memory and CPU cycles.
For high quality pitch detections, I prefer phase locked loops. With some intelligent time constant management you can find a very good trade off between response time and accuracy.
Of course, it all depends what your specific application requirements are. For some applications a DFT based algorithm is "good enough" especially if you have to do a DFT anyway.