My guess would be that the feeling is probably due to some combination of sunk cost fallacy and maybe that the writer would tend to feel some type of emotional connection to whatever they've already written since it's a reflection of their opinions / at some point when they were writing it they thought it was good stuff. I looked this up and found other people who do the same; in this post there's a lot of discussion in the comments about this, if you wanted to take a look.
I personally don't write that often, and the system of keeping the deleted chunks in Apple Notes was just out of convenience. Other people in the post linked above have used a Word Document to keep the deleted chunks, but I personally feel that it takes more time to open up a Word Document than to drop something in Notes, which is also particularly nice since you can always start a new note without having to scroll past old writing.
I never really thought of using version control before but I do feel like it's not quite the same as just keeping the deleted chunks. Usually I might delete a large portion, make some significant changes to another portion, and then go back and decide I want to use stuff from the deleted portion, so version control might be inconvenient since I've already changed other things too. I might be wrong since I haven't really used version control before, though.
When I revise my writing I find it hard to delete large chunks because it feels like a waste and I'm also worried that I might change my mind and need parts later.
I have a folder in Notes called "Writing Stubs," where I dump the would-have-been-deleted chunks (and also other temporary relevant bits of information, kind of like working memory). It makes me feel better that I have the original still and so, feeling more assured, I can ruthlessly delete large chunks from my writing which might be unnecessary or badly written. Speeds up the revision process.