When I cut off my selvages, I usually leave almost a 1/4 inch of white on the fabric I will be using. If the printing goes to the edge, I just cut off the very edge where the fabric is thicker and seems to want to shrink. If making binding, I can leave almost all of the white on, and put that where it will be folded over and covered.
Do I save what's left. Of course! LOL Those are strings for gardening, to hold up my bird feeder and fly trap, to tie up morning glories, to tie up packages and bags of batting. They are very strong. I waste very little, but I try to keep things organized so I know where to find it and it doesn't look like a mess.
When the season is over they can go out with the greenery.