I was once involved in developing a system like the one you describe, and it turns out it's a really hard problem, because for most non-trivial articles you want to do more than just skip a paragraph: you cut an explanation here, which means you need another word there and possibly that sentence doesn't make sense anymore so you'd rewrite that... and as a result, as a copy editor, you very quickly lose track of the flow of a story if there's two or more different variants all merged into one.
You mention elsewhere that "It potentially saves copy editors a lot of work." but I think you'd have to be a pretty darn good copy editor to keep multiple versions of a story in your head at the same time and ensure all of them keep their flow and coherence. Perhaps it really just is faster to read and edit any and all versions of a story separately.
What you're describing could work, but only if people changed the way they wrote to make it easy to cut things out without having to rewrite other things. But then you're back to something like the inverted pyramid.
What we ended up doing instead was to give authors the ability to "fork" stories into different editions that are, from that moment on, edited completely independently from each other, but behind the scenes keep track of which parts of the story are still the same, so you can provide intelligent diffs, notifications and potentially even merges like "In the web edition it talks about a guy named Jon but the print edition refers to John -- which is it?" without changing the experience for writers and editors too much.