Is the STFT a good solution to guitar monophonic pitch detection?
No.  An STFT is not only not overkill, it is not enough to find guitar "notes" reliably.  An STFT measures energy at selected spectral basis frequencies.  But a note usually refers to psychoacoustic perceived pitch, or pitch frequency, which is very often not the same as the spectral frequency peak, especially for guitar notes.  Guitars can produce more sound power at various (potentially slightly inharmonic) harmonic frequencies than at the perceived pitch frequency.  Also, the STFT basis vector frequencies may not accurately correspond to any of the musical frequencies of interest (being between them instead).  

Try looking up pitch detection/estimation algorithms instead of using an STFT or bare FFT magnitude.