Many reasons why a deaf person can use a service dog. Imagine not being able to hear smoke alarms, doorbell, baby cries, etc. It allows them freedom to go out, as the dog is aware of the sounds around them.
True, great danes are big but they are not "in your face" dogs. They have a calm temperament, low prey drive, not excitable, don't need a lot of physical exercise.
This woman and her "fiance" (she called him that in an interview with CBS I believe) are both deaf. The couple have 2 daughters. Nowhere was it said that the dog had been out of control on the flight.
Still though we know how much room there is not on these airlines. They should have paid for the dog to have his own seat not crowd other passengers. I understand this man’s complaint. In the future the airlines need to force this if they are not going to give more legroom, which we all know they are not.