Anyone who decided to make a catalogue for any decent enough library found that out on the first day.

(By “decent enough” I mean breadth. If you are strictly collecting some genre products from a small number of commercial publishers, you might be in the walled garden where everything just works.)

SBNs were introduced when, in addition to existing mass production, mass accounting and storage management for each item became possible (with computers). Outside of the centrally controlled environments they don't work well, or mean much. Sure, national authorities make enough rules about having proper ISBNs, but they do get ignored.

There are small university/gallery/collective publications that have bigger print runs than “official” books on some specific topic. There are books that are uniquely made or uniquely altered, and therefore can't share the identifier with another item. Most common example is getting an autograph — you probably want to know precisely where you've put the copy of Bible signed by the author, not just any other Bible that looks the same. Some people oppose ISBNs for political reasons, and either ignore them, or invent bogus numbers.

Then there's International aspect. Soviet Union, for example, did not use ISBNs until the very last of its years. There are still many books printed there — including complete works every scholar needs to reference — that never had any ISBNs.

Some works have been published for that last time a century ago. Some of them might had been immensely popular back in the days, but now they are forgotten. Others have been re-printed, but you've managed to get the first printed edition, a small book of then-unknown author. Those also won't have ISBNs.

So the idea itself that any book must be an interchangeable product from the batch in which each item has the same effect, and therefore can have the same identifier, is a bit narrow.

Obviously, professional librarians could instantly tell you that ISBN is merely one of the search markers, and is not the way the inventory is kept.