I have never seen waterfall in pure form. Mostly some kind of big upfront requirements projects with implementations iterations and a lot of project change management during the dev phase. These upfront requirements periods could be anything from a couple of weeks to a couple of years. While, I don't doubt that long requirements phases can have some value in aligning stakeholders on a new direction, they often became a raison d'être for complete teams - often stopping other promising projects in its wake: "You have to align with project jabberwocky before we can sign off your project." Agile seemed like a way to start early and get reduce the inherent waste by building software on paper upfront.