Airline is based on a BBC program that focused on a couple of British airlines, and one specific airport. The American version of the program could only secure the cooperation of the one airline, Southwest Airlines. All others refused to allow their airline to be featured. Southwest's philosophy must be that any publicity is good publicity. If nothing else, the show has generated an incredible amount of interest on the part of people wanting to work for Southwest, though I can't imagine why.
To be fair, Southwest doesn't come off looking that badly. They do have to make some very difficult decisions, and I think a lot of people realize that. Also, what is clear is that the program is exposing a lot of viewers, such as yourself, to the realities of the airline industry. You say you've never heard of booking a flight 3 months in advance, arriving at the gate to find that it was overbooked and you can't get on as a result, yet it is very common, especially on budget carriers like Southwest. What's worse, and again this is made clear if you watch Airline a few times, is that Southwest tells displaced passengers that they have a choice between waiting for the next Southwest flight or getting a refund, because Southwest, unlike all major airlines, doesn't have any inter-line agreements, so will not accommodate you on another airline that may have space. While it makes them look bad, I suppose, it does raise awareness of the situation, so that perhaps it reduces some future passenger's level of dissatisfaction at the gate.
Southwest is a budget carrier and very deliberately so. They may get a lot of flack for their poor customer service practices, but keep in mind that they have the best customer satisfaction ratings. You may wonder how that could be possible. It is simple, really: Customer satisfaction is a matter of how well you satisfy the expectations customers place on you. If you prepare them for a certain (low) level of service, and you charge them a lot less than others would have charged them, the passenger will often be satisfied with a lower level of service, at least as compared to the situation where you inconvenience a passenger after charging them an arm and a leg!