1) Why are you assuming this is an ESA?
2) the airline DOES have recourse here, the law allows them to require people to buy extra seats if the passenger and their dog doesn't fit into the space allocated for a single seat.
The law says they do but my understanding reading the request from Airlines 4 America is the enforcer (DOT) muddled things in 2009 by offering guidance that implied an in cabin accoodation request with other passengers should be made first.
They’re trying to get that clarified - I’m guessing they’d love to charge for the second seat more often.