We continue to train "owner trained" service dogs with a local VFW program that supports our combat veterans by helping them train their own service dog. We allow them to test an existing pet to train. If they pass our tests, they would be eligible to train for the program at very little cost to them.
However, that said, service dogs are born, not made in my opinion. That is why we work so hard at providing health tested, OFA certified puppies to send to training.
Some of the reasons a dog might not be appropriate for service dog training:
Too ball/squirrel focused.
Not socialized to other dogs and people. May be fearful.
No health clearances (while this might not be a stumbling block, they must be aware that if the dog is in service and has a health issue, all that training will be lost). They would need to start over with a new dog.
Lack of interest in doing the job.
So you see, there are a lot of reasons that not just any dog can be a service dog. But we are willing to try! Some do succeed! But owner/trainers need to be committed to the year to year and a half it takes to train a dog to have public access and be a good service dog!
All dogs can be emotional support and if that is what they need, that is ok too.