It's really natural!
- make a bunch of edits
- decide I don't like all of them
- copy the part I want to keep
- undo a bunch
- paste the good part
This is copy, not cut, but it wouldn't work if the clipboard state was part of the undo system.
Exactly, you've nailed it.
The article isn't arguing that clipboard state should be part of the undo system, it is arguing that cut shouldn't touch clipboard state. In the "Side effects" section they mention if you want the contents to go to the clipboard, then you should use copy instead of cut.