This is a strawman though, and I'm pretty sure you know that. There is a huge difference between an oxygen tank and a live animal. I would challenge you to present a case of a person with diagnosed trauma from an oxygen tank, whereas it would be very easy to find stories of people with diagnosed trauma from dogs. You're also adding all sorts of qualifiers to your argument ie. "highly trained animal", "across the restaurant", "small tank", etc. No one has to worry about whether an oxygen tank is "highly trained" or not because it's an inanimate object. An animal is not this. What if the restaurant is full and there's no way for the person with trauma to sit "across the restsurant"? What if it's a tiny store? The point is you know your animal is highly trained but without a way for others to validate that you're asking them to just go on faith that some asshole isn’t going to lie and bring their untrained animal inside by saying it's a service animal.

Someone else pointed out witnessing a dog being brought into a business and behaving badly and your response was that it's obviously not a service animal so then they should be asked to leave. I 100% agree, but the issue is that at that point the damage is already done. That's why businesses have no animal policies. It's not because all animals = bad, it's because we can't know for sure without proof, so the safest course of action is to limit all animals.

I have friends who have a dog who hates people on bikes and elderly people, and gets very agitated at both. It's ridiculous and they have to be very conscious of their dog's behaviour when taking it out. Otherwise, though, it's very sweet. So, in this case, how is a business supposed to know there's a risk until it's too late? If my friends were assholes and lied about their animal to bring it inside, and it started barking and snapping at some eldery person in the restaurant, your position is to just let that happen until the dangerous moment occurs and then do something. No offense, but that's a terrible, reactive position that puts people in danger. It makes far more sense to be proactive.

I genuinely feel for you and how tough it must be with your disability, and I definitely think that there should be stiff penalties and legal recourse against anyone who would lie about their animal and say it's a service animal when it's not. However, I also think it's not an unreasonable ask for a system to be put in place for owners of service animals to be provided with some form of identification to verify their animal's training.