Unfortunately Delta's hand is forced by the gov't here. While carriers aren't required to carry an animal that doens't fit under one seat, the interpretation of the law by DOT in 2009 confused things by putting the onus on an in-cabin resolution, rather than a pre-boarding resolution to handle animals too large to fit in front of one seat.
Delta can ask other passengers if they are willing to share space with the animal in the same cabin. If there are none, then as the last resort they can ask the animal owner to take a different flight. But the onus to complain is on the passenger seated adjacent.
https://cms.dot.gov/sites/dot.gov/fi..._5_13_09_2.pdf
"What should airline personnel do if a passenger with a disability is accompanied in the airplane cabin by a service animal that does not fit in the space immediately in front of the passenger and there is no other seat in the cabin with sufficient space to safely accommodate the animal?
Answer: If a service animal does not fit in the space immediately in front of the accompanying passenger with a disability and there is no other seat with sufficient space to safely accommodate the animal and its partner (i.e., user), there are several options to consider for accommodating the service animal in the cabin in the same class of service.
The carrier should speak with other passengers to find a passenger in an adjacent seat who is willing to share foot space with the animal, or a passenger in a seat adjacent to a location where the service animal can be accommodated (e.g., in the space behind the last row of seats) or adjacent to an empty seat, who is willing to exchange seats with the service animal’s partner. As noted in the preamble to our rule, there are probably no circumstances in which the purchase of a second seat would be necessary to accommodate the service animal. If a class of service on a flight is totally filled, there would not be any seat available for purchase. If the class of service had even one middle seat unoccupied, the passenger with a service animal could be seated next to the vacant seat. It is likely that even a large animal (e.g., Great Dane) could use some of the floor space of the vacant seat, making any further purchase by the passenger unnecessary.
Only if there is no alternative available to enable the passenger to travel with the service animal in the cabin on that flight should the carrier offer options such as transporting the service animal in the cargo hold or transportation on a later flight with more room. When transportation on a later flight is offered, carriers are strongly encouraged, but not required by Part 382, to allow any passenger who wishes to rebook on a different flight to the same destination and on the same airline to do so at the same fare."
There is a fresh look at the rules happening right now. And the airlines' lobbying group wants DOT to make clear airlines have the right (already in the law) to refuse transport of animals that don't fit under the seat,
which would open up the doors to resolving before boarding:
https://www.regulations.gov/contentStreamer?documentId=DOT-OST-2018-0067-0093&attachmentNumber=1&contentType=pdf
"
It is self-evident that it would “fundamentally alter” the service provided to the adjacent passenger to deprive that passenger of his/her foot space and obligate or pressure the passenger to share the space with an unfamiliar animal and the need to even make such an inquiry places airline agents and flight attendants in an uncomfortable position. DOT, in clarifying in its Final Statement that carriers are not required to accept animals that do not fit under a single seat, should revert to guidance that existed prior to 2009. Because this is a “guidance” issue that is not contained in DOT’s regulations, DOT can and should address this issue in the Final Statement; it would be neither necessary nor appropriate to defer action on this issue until the conclusion of the rulemaking."
Hopefully things will change to better balance needs, and also reduce fraud (no evidence of that in this case - that's another discussion).
Southwest's handling of passengers of size is an interesting one. They ask them to book a second seat in advance. They then refund the cost of the second seat after travel (presumably for the agent to verify it's needed).
https://www.southwest.com/html/gener...olicy_faq.html
If there were less fraud in the system, this kind of airline initiated policy might be viable for true service animal needs.