SFGSSD- I can understand where you're coming from but as the handler of my third service dog and being in the middle of training my fourth I respectfully disagree that it is an undue burden on the dog to also fill the role of Therapy dog. It is the duty of the handler to make sure that their dog is not stressed and that their training and behavior doesn't slip but that needs to be a choice made by the handler based on their dog.
And it really is a case by case issue... my current dog loves to work and is completely handler focused but in most cases could care less about other people. He would get no joy and a great deal of stress if I forced him to do Therapy work.
My service dog before that loved people and her greatest joy following service work was making people smile. She was very active in therapy work and brought a lot of joy to a lot of people and I hate to think that that could have been denied to her by people who made blanket policies.
Each dog is different, and depending on the dog there's no reason that they can't enjoy being there for other people when they are off duty.
A handler may not always have the training that the trainer does but they are the ones who live by their dogs and must be completely in tune with their dog. No matter if they're owner trained or trained by a program the handler should have the information to make the best decision for themselves and their dogs.
I've been a service dog handler for a very long time and apprenticed with some of the best trainers on the east coast in my opinion, and I think it's wrong for a therapy dog organization to make a policy that would keep one of my dogs from doing something that they love.