I use distilled whenever I mix chemistry, and I use it for final wash (along with Photo Flo).
The advantage/my reason for doing so is that it doesn't have the dissolved minerals/dirt/permissible levels of toxic refinery runoff that the tap water has in it, so it eliminates a consistency-obstructing variable. When I lived in North Texas, our tap water came from a lake, so the dissolved solids profile would change radically throughout the year.
I don't know if it had any discernible effect on my negatives, but the more variables I have control over, the closer I am to total consistency.