This. Plus, it's not really fair to subject the general public to a dog that isn't actually necessary. Disabled SD handlers get to use their SDs in stores because it mitigates their disability and gives them independence. This is something the public just has to deal with. SDs are far from common - I very rarely see another SD when I'm out. If SDs were "common" then people wouldn't freak out so bad every time they saw one. Asking people to deal with an impeccably trained dog in a store once in a while for the sake of someone's independence is different than asking them to deal with a store full of "well trained" (or not) pet dogs just because someone wants to take their dog with them for shits and giggles. People with allergies or who are afraid of dogs can currently avoid SDs pretty easily. That's not the case when everyone brings their pet dog to the grocery store with them. What then?
Plus, the whole lying and breaking the law thing. There's that.