In general, are check digits common in schemes like these? Is it something you'd do if you expect lots of manual copying, or scanning or other potentially-error-producing conversions?
Upon a quick reading of the Wikipedia article on EAN-13 it appears that there is some parity to determine the direction of the scan (i.e. upside-down or upright) but the numbers are encoded as-is without any further error correction contrary to e.g. QR codes.
Alas, for a definitive answer on the reasoning one might have to buy the relevant ISO standard, if it is even described there.
Given that human adults are said to be able to keep 5-9 items in working memory, I would think it prudent to include a check digit for the ISBN when one might be required to manually enter them into search masks, forms, etc. and if only hearing it (e.g. over the phone) might not benefit from the grouping they visually gain from the interspersed dashes.
On the topic of correctly copying (manually):
whenever I have to be certain to correctly transcribe a long important number or string I would at the end cover up both the source and the transcription, then reveal one character from the end, then the second to last on e.g. the source, verify that the last and the second to last on the transcription matches (in that order!), then uncover the next 2 on the transcription, verify against the source, continue with the source and so on. This helps immensely to discover transposed digits (especially since my mother tongue is German where we swap the tens and ones while speaking (or thinking with the inner voice) a 2-digit number) and not glance over well known digit groups such as zip code or special dates, etc.
And International Bank Account Numbers (IBANs) have two check digits, but at the front, not at the back. And having check digits is important, because it might not be easy to get your money back, if transferred to some unintended account.
The IBAN consists of up to 34 alphanumeric characters comprising a country code; two check digits; and a number that includes the domestic bank account number, branch identifier, and potential routing information. The check digits enable a check of the bank account number to confirm its integrity before submitting a transaction. https://en.wikipedia.org/wiki/International_Bank_Account_Num...
Lots of examples at https://en.wikipedia.org/wiki/Check_digit
But for books, the worst that can happen is that you get the wrong book. Maybe back in the days when people ordered books via phone it was good to have a checksum, but even then the seller would probably read back the name of the book. So I don't really see how it's necessary here.