Realistically, I'd rather see a standard that specifically names what animals can be used as "service" animals, as well as a requirement for some sort of certification. And I would like to see the concept of "comfort" animals eliminated under the law, because IMHO that's the one that people are abusing.
Your first part has already been done. Under the ADA your choices have been restricted down to dogs and miniature horses. Cats, pigs, monkeys, regular sized horses, and all need not apply. Monkeys are no longer allowed because they're considered too dangerous, and too smart - it's cruel to keep them as a service animal.
As for the comfort animals, they typically aren't actually protected, it's more that there isn't a specific listing of what conditions it applies to because it would be too damn long. Blindness, deafness, seizure, panic attacks, paralysis(fetching, toting, opening doors) are only the start of reasons to have a service animal.
As such, people pushing it generally get away with it because the people in the location don't want trouble and aren't familiar with the exact details of the law.
As usually happens, something starts out as a response to a legitimate need, and as soon as the .gov creates a protected class a metric boatload as arseholes start claiming that their pet orangutan is a "comfort animal" and that every place of busness or public accommodation or government office MUST allow the beast in.
Which is why I support requiring them to pass tests on social behavior regardless of "legitimate need" because it gets down to the point - if you're going to have the animal out in public on and off private and public land, it needs to be well behaved. Don't worry about what task(s) it has been trained to do on the medical side, that's hard to assess. Whether the thing can be out and about without tearing people's faces off is the more important concern.