I think all of this depends on what the dog is used for and how knowledgeable the handler is.
So from a professional service dog organization point of view...they are providing dogs to people that might not be super dog savvy. They're giving dogs to people that possibly have never trained a dog, have never taken care of a dog, and don't really understand a lot of the signals a dog might be giving off. They might not be able to see the "degradation in training" because they don't expect the same high level 100% of the time. It makes sense...some of those people begin to see their dogs as pets and if the dog doesn't listen the first time, or gets distracted but then 10 seconds later does what its asked to do, they won't care. I do this all the time with my dog (not SD)...in training or at a trial I expect 100% obedience, but at home if he doesn't sit within 2 seconds of me saying it, I'm not really going to punish him/correct him.
Now for the handler trained SD...those handlers are probably way more knowledgeable than most people when it comes to dogs and dog training. They have raised their dog, trained their dog, and due to that have a much better understanding of what their dog is capable of without increasing it's "stress" levels.
So if you as an organization want to ban all of your handlers from using their dogs as TDs, its your prerogative and I can see your reasons for it, but to make it a law or a nationwide rule...I don't think its necessary. When it comes to the dogs YOU train, it really is your responsibility to keep them working at a high level, but when it comes to the dogs other people train personally...its kind of up to them what level of service/obedience they expect.
As to TDi and all those other organizations...they can not register SDs all they want. All the handler has to do is say their dog isn't an SD and their dog is registered. Not like there are any SD registries that the TDi references. Also...the majority of the places I've done "therapy work" at, don't even require a registration of any sort. They take our group's/handler's word for the fact that their dog is safe for this type of work (our group wouldn't allow them to go if we didn't think they were).