United needed to offer free tickets anywhere in the United States. Start with one. Then add a second ticket. Then add upgrades to that ticket. Then add Hawaii. The reality is that half the plane would take the 2 tickets with a cabin upgrade. That’s a free ticket with your wife. Add first class to it and you will have to beat people off the plane. Another thing they used to do in the old days was to give away first class vouchers, another wildly popular choice.
Whether you have business travelers or not on your flight, whether you have people going home or leaving your home, means you will have different appeal to your offers.
One blogger - a United airline pilot, also suggested that the gate attendant in charge could have told the pilot to announce to the boarded plane that unless more passengers volunteered to accept the money offered to take another flight, that the flight would be cancelled altogether. I think that might have scared up some volunteers, but have no idea if it would have not resulted in a PR headache of a different kind for United.