The other downside to these free (just about always) and discounted (sometimes) ISBNs is that they link the publisher as the service you got the ISBN through, rather than yourself, even if you're doing what would classically be considered a self-publishing job. How big of an issue is that? IANAExpert, but it seems like there are some nooks and crannies of IP law that can be swayed by owning the imprint, but little practical concern for the average person putting an ebook on Amazon e.g. Perhaps someone with more in depth publishing knowledge can color the risks better than I.
Edit: HN throttling, can’t reply. What if the Internet Archive gets a block and hands them out via Open Library? They seem positioned to argue they’re a bonafide publisher.
That is indeed a bit of a ruse, since an ISBN is supposed to identify an edition or format, but not the sales channel. We give our epub files an ISBN, and all the vendors that sell that file (including Amazon) use the same number. But when you publish with KDP, you are not the publisher. Amazon is, so you have less say in the matter.
Good point on the "publisher" linking caveat though. I don't know much that matters in this day and age? Would be useful to learn from some published authors.