I know someone who did this for years. It worked great for her until another person who did it was eating the produce, got sick and sued. (Ridculous) All the stores quit doing it after that. But it's a great idea, and all you can do is try. If the big chains won't allow it, maybe try the mom 'n pop stores.
It's a lot of work, cuz sometimes there is food in plastic bags, and sometimes other garbage so you have to go thru all of it. The people I knew who did it supplied their own 50 gallon plastic drums, and picked up several times a week. They had cows, chickens, emus and rabbits, and everyone was happy campers!
They sold a lot of their animals when the grocery stores stopped doing it, cuz feed costs were so high.