"Continuous Delivery", huh? Yeah, let's replace one consulting fad (the 4 or 5th I've seen in my career, I entered when "Waterfall" was still in vogue, then XP, then Agile, some variations of each too) with another. How about this methodology: http://programming-motherfucker.com/
People tell me that waterfall was never really a thing, and it was only ever a name for how things should not be done and that nobody ever actually advocated it. Is this not true? I'm too young to remember what came before agile.
The thing to remember though is that the 'pure' version of the process (in which you never return to the previous level - hence the name 'waterfall') was regarded as an ideal, not as something achievable. Nobody expected that there would be zero bugs found in testing that would require more coding work (why test otherwise?), but it was regarded as a kind moral failing, to be met with a lot of hand-wringing about why we can't be like real engineers, who never make mistakes &c. And the same applied to revisiting the design or requirements phases.
The next level of idealism held that even if avoiding returning to a previous stage was impossible, you could at least limit it to the immediately preceding stage. As Royce pointed out in the first paper to provide a convenient diagram of the established software lifecycle to cite, this never happened in practice either.
Over time the necessity of doubling back became less of a moral failing and was incorporated into the teaching of the process, without any acknowledgement that the entire concept was fatally flawed. It was also succeeded by several iterative but still waterfall-like processes (starting with Royce's paper and eventually followed by Spiral and RUP). Thus there are many folks who still believe that the pre-Agile process (they may not recognise that there was more than one) was just fine, and that the pejorative 'waterfall' was applied to something that never really existed. In a certain sense that's true, but it gives a completely misleading picture of the history.
Agile's contribution was the idea that any or all of the phases could be happening simultaneously - and, more importantly, that was OK. Plenty of people had been ignoring the orthodox methodologies and working that way, of course, but don't believe anyone who tells you that was an orthodox idea before Agile.