So how long would you expect books bound this way to last?
I took some pictures of the ones I've made for reference: https://imgur.com/a/60zP8vn .
So far, none of them have come apart but I'm pretty careful with my books.
With cheese cloth and library tape? Many years. If there is just the gum on the binding (no tape or linen binding) then a couple of years with light use, less time with heavier use. One of the things that the binding class taught was that books would be rebound several times in their lifetime. I've rebound at least a half dozen paperbacks that eventually started dropping pages (became detached from the binding).