I'm not sure it's so much feeling like using a food stamp but, in a restaurant with a server, using a coupon is just an awkward transaction. You have to lay it out on the table before the meal to make sure the server knows you have a coupon, i.e. you have to sort of make a big deal about it. (Over and above any issues with the server now suspecting they might get a crappy tip.)

For a more conventional purchase situation, you just hand over the coupon with your credit card and things are taken care of in a very transactional way.