Every phase of the project has iterations, but iterations stress different things (requirements in the beginning, construction and handover in the latter phases).
Tragicaly, it's not a strawman, it's an enshrined project management method the DoD created from a misunderstanding of Royce, which escaped into the wild.
Now, most people who say they do Waterfall are quite mistaken. They don't, they do some sort of iterative method as you say. But they report as if they have distinct, linear phases with distinct linear steps, as if Waterfall were the reality and not an imagining. Which is itself problematic. This means that upper managemnet comes to believe that Waterfall works because they see it working, not realizing that the reports themselves are misleading.
Everytime one of the project managers tells me they're doing Waterfall I press until they admit it's "Modified Waterfall", by which they mean the V-model or Spiral or other models with explicit feedback loops/mechanisms. And it frustrates me to no end that they keep using the wrong terms rather than the precise ones, because now upper management has begun enshrining Waterfall again after two decades of improvements. Now we have to fight the same battles, to impress upon them that iterative methods are what we actually do, and that a strict linear flow is impossible.
Some anecdotal evidence that waterfall is not a straw man: at least 10 years ago, waterfall was taught as waterfall without iterations at some German universities. This was the starting point, and many derived models, like the V-Model, where also taught, but iterations we’re nowhere in sight.
Every phase of the project has iterations, but iterations stress different things (requirements in the beginning, construction and handover in the latter phases).