There are already laws in place about what qualifies a dog as a service dog and where they are allowed to go. We don't need new laws because we already have laws. They are just not being enforced very often.
Under the Americans with Disabilities Act, a business is allowed to ask two questions when someone comes in with a dog. Is that a service dog? What tasks is the dog trained to perform? If the handler answers yes, it is a service dog, and is able to say what tasks the dog is trained to perform, the business is supposed to take them at their work and allow the dog in.
Sure, people could lie and say there pet is a service dog. They might make up something when asked about tasks, but I think that question would stump many fakers. So simply asking the two questions allowed by law would screen out some fakers. Not all, but some.
Now, under the ADA, businesses are allowed to ask a handler to remove a dog that is not housebroken or that is disruptive or behaves aggressively. But often they don't.
If they did, though, I think people with poorly trained dogs would soon stop taking them places. I mean, why drag your pet dog to the store every time you go if every time you were asked to remove him? That would be a big hassle. You'd start leaving Fido at home, right?
Some states also have laws making it illegal to misrepresent a pet as a service dog. I don't think those laws are enforced much, if ever, though. But they could be.
Wouldn't it be easier to enforce existing laws than to pass and enforce new ones?