I think the bigger problem is that there are no real clear requirements for what constitutes an animal that that supports your emotional illness. Can you just re-purpose the family pet? Buy a collar on amazon and call it a service dog without any actual training.
When it was just blind people, it was pretty legit. Those dogs are some of the best behaved animals you will ever see, and are specifically trained on how to act when in situations where dogs are not typically allowed.