Lately I've been trying to play clean without muting to see what the root cause is for all the noise.
I've found that if you play a note and release it too slowly, there will be buzz because the string is partially fretted for a short time. If you release faster, the noise goes away. If you release TOO fast and the finger leaves or nearly leaves the string, you'll get the open string noise AND when you add pressure back, you'll get noise at the fret, too. These types of noises are really amplified if your finger is in the middle, between 2 frets.
When you move the finger up against the fret, the noise that you get when letting off the pressures is greatly reduced, even if you let off as slowly as you can. No muting and the note shuts off. The plucked note is a little less bright if you are too close or on top of the fret.
Some chord grips or fast phrases make it difficult to keep the fingers right up against fret, so you still have to deploy the right and left hand to keep the noise to a minimum. But it is interesting how much noise control you can achieve without any extra muting with long single sustained notes.