And they are unloaded onto something that can transport them out of the way. Even in the desert, after 3,000 or so containers, finding room in the big pile to unload number 3,001 without moving the crane to make a new pile might be problematic.

This video really shows the process up close:

https://www.youtube.com/watch?v=kj7ixi2lqF4

Yeah, and those systems are fully automated too - years if not decades before e.g. Amazon started doing something similar in their warehouses. Mind you, containers were standardized in the 60's so there's a bit of a head start there.