I used to work with a bass player who had a custom job (by Ed Reynolds, then of Soundsmiths in Chicago, now of Ed Reynolds Guitars in Austin - a top-notch luthier.) He actually had Ed put peizos under the fretboard (IIRC, 3 of them - 1st, 12th & 24th frets) just to pick up fret noise - what he called the percussiveness. Sounded like crap. Fortunately, they had their own volume control, and none of 3 bands I worked for him in played anything that he could use them on.
(And he then unhighjacks with...) Of course, if you want to do away with fret noise entirely, you could always get rid of the frets.....
Peter