Since service animals are already allowed, the issues relative to allergies to dogs/cats/whatever is not really valid. The animals can already be there. Most service animals are well above the 20 pound animal as well. Just because Fido stayed home does not mean the Fido-owner did not have some quality lap time with Mutsky for a goodly time before leaving or give the hound a good hug and experience a good face licking just before walking out the door. Since exposure to an animal that sets off the allergy can be and probably usually is unexpected, the person must always be prepared with an epi-pen or whatever their short acting anti-allergy medicine is. And as noted, the exposure could be second hand, not direct exposure.
The reason that pet carrying ended was two fold: One, the SPCA and others got regulations put in force requiring climate control and other features not practical on trains. The other was slob pet owners. The restrictions on carrying animals in baggage cars is close to being an example of the saying that, "The road to Hell is paved with good intentions."
Sarah, as to not subjecting a pet to carriage in airport baggage compartments, that is not as simple a decision as it may seem. We did it three times. First, was a transpacific move. Our 16 year old dog had never know life with anybody else and was thoroughly bonded with the family. The final decision was that bringing her with us was the better choice. It took here a couple of weeks to forgive us, but she ultimately did. The other was a four hour trip each way after a not so happy for her experience at a pet motel, and not a cheap one, either. Being able to carry her in a cage or on a leash for a 4 hour trip would have saved several weekends of car rental.