I can't help wondering if I've missed the point of Waterfall...

The point of Waterfall is to prevent change. This is because change is expensive. It's much cheaper to make a change at the start of a project, when you're safely in an office and can type those changes into the computer (in a requirements document) than when you're actually building the software out on the field and have cranes and concrete and rebar and safety inspectors and a 200-foot hole in the ground and the customer comes out and says "Wait, I really wanted a nice two story building instead of a skyscraper!"

If someday we can make it as easy to write computer programs as it is to type clear and unambiguous and testable specifications into a text editor, maybe Waterfall can go away.