It's already done, and yes, they do. Part of my bookkeeping job is sorting the store coupons (from our own flyer, which are just trashed) from the manufacturer's coupons, and I see quite a few printed from online coupons every day. Probably only 5% are printed, but it's a start.
Now, in all honesty, I'm like most people: I'd rather see them just lower prices and quit wasting my time with the coupons. But if that's the game, I'll play.