People can get animals for whatever reason they want, people can get a dog if they want and be environmentally friendly if they want I never argued against any of those things although you seem to frame my argument as if I am.
What I mean to say is, in this very specific scenario, if you know that your chosen form of transport does not allow dogs (for whatever reason, you dont get to make the rules regardless of whether you agree with them), and theres no other suitable alternative you are happy with for environmental or price reasons or any other reason, then you shouldn't get a dog.
The solution to the subway not allowing dogs isnt to get a dog and demand or cheat to be allowed to take it on the subway, its to take an alternative or not to have a dog in the first place.
Although i made a few points about why dogs may not be allowed on the subway, that is still not actually the issue. I mentioned allergies as a throwaway example of a reason that you may not allow dogs but im not trying to argue with you over how many people are allergic to dogs and whether its justifiable tk ban them for that reason.
It doesnt matter WHY you are not allowed dogs all that matters is that you are not. Respect the rules. Its not your train so abide by the rules of the train you are on. Maybe there are millions on the subway that would like to have their dogs with them but they don't, because they respect the rules and are not entitled assholes like the OP.
If you don't like the rules then find out a legitimate means of changing them, I wouldnt know if its local government or private transport companies who run the subway i don't know enough about NYC to say but whoever it is then find out how you can make suggestions and do it via legit means. Im sure if theres enough support things might change.
There is no situation where the correct thing to do is to lie about your dog being a service dog and brazenly flaunt breaking the rules just because it suits you. Thats selfish and entitled behaviour.
Imagine a scenario where someone invites you to their home and they say that dogs arent allowed. Now you know they are not allergic or afraid of dogs and tou nnow your dog is not badly behaved or going to cause any fuss or mess. You may think that it kinda sucks you cant take your dog, however you still have to respect the rules of the host. If youre not allowed the dog youre not allowed and if you turned up with the dog in a silly vest that you said gave it entry privilege that wouldnt change anything.
The solution is to either go to the home without the dog or to not go at all. Apply the same reasoning to the subway. Dogs arent allowed to either dont take the dog or dont take the subway. Its pretty simple.