Your logic is perfectly reasonable and sound, and it took me many years of working for Big Corp (TM) to understand that is simply not how a big corporation thinks.
Once they have a revenue stream, anything that diminishes it is a "loss", even if that revenue stream was kind of fake or invented anyway.
The massive company I worked for was making millions per week from something that was accidental and they shouldn't have been. But it went on for so long, they got so attached to it (those millions looked great on year-end reports) that soon any talk of "fixing" the problem was referred to as a "revenue loss" and it was completely unacceptable to the business, unless your proposed change kept the revenue.
The particular incident isn't really a good one to base discussions on, it was so egregious that the discussions are boring. It shouldn't have happened.
There is a more interesting discussion to have about overbooking, whether to allow it and how to deal with the situation where they get it wrong and don't have enough seats. Maybe the minimum payout for denied boarding should be higher. Maybe the airline should have to start their offers for voluntarily taking a later flight at that price. Maybe the sale process for all tickets should include an option to actually reserve the seat (for a fee).
But there isn't a discussion to have about whether a business should call the police to beat up a customer that they just don't want to serve.
We're talking about how companies view the loss of "extra money" as a loss of revenue, when in fact they are already perfectly well making all the revenue they were before they invented the "extra money".
Air travel is fantastically expensive and we all want it to be cheaper than it really is. This is one of the ways that is done (people who don't show up pay for other people and displaced passengers move to underfilled flights).
The practice is annoying, but I think with the exception of bungled reqccomodation is a net plus for the consumer.
"Empty seats cost the airlines money, and they need to recoup those losses somehow."
What does this mean? The issue here is overbooked seats. If a seat is physically empty during the flight because the passenger just doesn't show up, the airline doesn't lose any money - the ticket/seat is still (pre)paid for. Overbooking is simply a way for the airlines to make extra money on top of what they would normally make, gambling on some percentage of customers not showing up for the flight.
So, is the airline industry operating on such a slim margin that giving up the practice of overbooking would force airlines to take noticeably drastic cost-cutting measures?