Bad things can happen when someone becomes more interested in preserving their 'authority' rather than solving the problem and task at hand. Humility can be a wonderful quality.
Yes, they have the authority to throw people off the airplane if they want or need to (which is their private property anyway--subject to conditions of carriage and law--which in this case they could). Yes, the cops (or kinda-cops) have the authority to use physical force (level of which depending on the threat) in doing so. But how they do so does matter. The reasons why airlines (and other transport modes) exist in the first place is because people want to go from point A to point B. So the pax are the reason why pilots, f/a's, maintainers, fuelers, schedulers, ground staff, managers, and support staff have a job in the first place. No pax, no airline, no profit, no job.
Plenty of blame to go around. United/Republic for boarding in the first place (and the subsequent decisions they made), pax for not leaving, the City of Chicago's pseudo-cops for dragging an old man around and banging him up.
Good judgment seems harder to come by these days. But good judgment can mean everything in handling even relatively simple situations which can escalate.
It's a
PR and litigation nightmare which will cost many times that of a chartered jet for the trip. Everyone gets sued, everyone sues each other, thrown off pax likely gets a hefty settlement from United/Republic and the city. Passenger got banged up, airline and cops get their image badly tarnished, airline and city lose money. People make fun of United on the internet and late night TV. Real losing situation for a lot of people. All over what was a relatively minor incident (made by lower echelon decision makers) escalating.
The lesson learned for me is it's wise to pay for people with good judgment (giving them coherent guidance, training, and leadership for the tasks they might face) and take good care of them because a bad decision in the trenches can cost you a lot of money at the top.