Strange, I didn't see your post above! That's good to know you found another way. My experience is the same as you. I couldn't really notice any difference at all. The pivot that you unclipped the bracket from has plastic sleeves in there as well so these probably get worn down as well over time. Does yours have any play there? I can move the bracket left and right a few mm's at the pivot point, is yours the same?
You can test by grabbing both ends of the pivot (the clip end and bracket end) and moving it side to side.