Sorry, I thought you were looking for a solution to not having to cut the bags hence using string. The idea stems from when I used to have a steel chain (ages ago) wrapped around my seatpost all the time. I'd use it like a makeshift rope when in such situations. I never felt confident that the bags would stay out of the spokes so I had to do some rather creative stacking and tying on the rack.
But you're saying this works safely? On all racks? I've got those old fashioned types (it's old). I just might have to try this out.
Thanks!