Dogs are the new designer children.
I dont think this is a vanity thing. I haven't googled it, but my *guess* is, that the rule was implemented as the result of a/some complaints of people who didn't have their large breed dogs under control and allowed them to bite/intimidate/get in the face of, etc other ppl on the subway.
as a dog owner, I'm well aware of the double standard society has for larger dogs. if a bigger dog and smaller dog get in a fight, ppl will blame the larger dog EVERY TIME, regardless of which dog started it. theres a strange tendency to humanize them and think that the bigger dog should be aware of its physical advantage and defer to little dog, otherwise it is seen as a bully. I'm not sure animals understand this rule. most bar bouncers don't seem to.
I'm also well aware that some inconsiderate/negligent dog owners do "ruin it for everyone" as well, and shouldn't be tolerated.
regardless, ensuring the dog is in a bag, forces the owner to exercise some control of their animal, and in essence weeds out those dogs that aren't calm enough to tolerate being in one.