I would do this all the time if I didn't have an f'n floating bridge (I never even use the vibrato bar so I don't really know I why I bought this guit. )
I mainly use nylon hose tied around the neck for leads (if they don't have open strings in them) or taping off unused strings for rhythms usually around the 12th fret or so...
I noticed it while recording with my Ibanez S Series. I got it used without the string "tree" and I noticed the strings above the locking nut were creating a resonance that was really annoying.
Honestly if they made a MAB String Dampener with seperate mutes for each string, I'd totally get one for the studio... maybe I should make one... hmmmm