I know most people might wonder why Los Angeles International Airport (LAX) is on the list, but I have encountered a number of people that have lived in California their whole life and have never been to the airport. LAX is not just any airport, it is THE airport. It the the 6th busiest airport in the World. It also handles more "origin and destination" passengers than any other airport in the world.
I've flown out of LAX countless times and have never gone without some kind of incident. With most airports that I frequent (MKE, BOS, ORD) I can show up within a couple of hours of my flight and have no worries about making my flight. LAX is always a crap shoot so I leave extra early. The airport can make even the most organized airline look like a disaster.
It's on the list because it is such a great opportunity to visit so many awesome places around the world by cheap direct flights. If planning to visit most countries in the eastern part of the world you can usually find a deal leaving from LAX. There are also a lot of places intercontinental to visit that are cheap. The northwest and the southwest all have spectacular destinations that are a pain to drive to but a hop on the plane from LAX. Outside of the airports in NY, I don't think any other airport allows this kind of access to travel. If you like to watch planes its ideal as well because a plane lands every 30 seconds.
Although it may not be always convenient to get through their internal logistics, it's a convenient place to get to other places.