That's not why coupons exist, though, it's just a side effect. If coupons didn't exist and your goal was to help poor people eat, coupons would be a weird way to do it.
Why is it weird? It's a lot like the 10c can and bottle levy. Ostensibly for recycling, but also gives homeless people a job. Sneaks under the radar of regular-sized market forces, and gives them some agency in their lives.
It’s pretty badly targeted. Lots of poor people don’t have much time, and lots of better off people have lots of time and enjoy things like screwing around with coupons to get a discount. It also doesn’t do much for extreme poverty. If you have no money, it doesn’t matter if you can get a coupon for half off a loaf of bread or whatever, you still can’t afford it. So you end up giving more help to people who need it less.
If you want to help poor people buy food, give them money to buy food.
