I think some worry that service animals that are owner-trained would be singled out and end up receiving less legal protection. My compromise is that whether the dog is trained by Leader Dogs to assist a blind person or by random-dog-owner to alert them of a pending seizure or panic attack, it really needs to have those core obedience skills down perfect and asking a person bringing their service dog into a business to demonstrate that their dog can sit, stay, and come, even in a chaotic environment is fair.
The ADA rules were purposely written to be very vague and there is language that establishes a sort of "When in doubt, interpret in way most favorable to the disabled person." and they have been hard pressed to answer questions directly on the subject where doing so could end up limiting protections for the disabled. And all of that is probably for the best.
Like there's a part of me that really has a problem with how the ADA handles this with regards to, for example, a specific question of whether a business must permit a service dog even when the business owner is severely allergic. The ADA answer is that service dogs are always permitted and employees with allergies should be relocated to another part of the store while the dog is there. Which doesn't address the situation of a small shop with just the allergic person working. But at the same time, this sort of conflict is going to be very rare and ... dang but my eyes work fine so if putting up with the occasional superfluous mutt is my "we live in a society" tax ... fine.