FWIW, I don't think large dogs should be allowed on planes either. A modest size dog is perfectly suitable as a service animal.
I have sympathy for legit need of a service animal. Not so much for personal fashion statements which would be impractical for me to own as a pet at home (I've got a full house with yard). At least not on airplanes which are uniquely confining, and you can't just stop and get off.