Unpopular opinion: real problem here is unreasonable restrictions on taking pet animals with you. In US it's a particular problem, because you can't make rules based on judgments on the spot. Allow pets in restaurants/planes, people would sue because you denied them service because pet peed all over the place or owner can't control their pet.

So, here we have blank prohibition on any pet anywhere, which is, IMO, worse than service ponies on a plane.