DOI does resemble ISBN, but I can find book info via ISBN without relying on the publisher to maintain a database.
(via Google or ISBN.nu or maybe even the Library of Congress)
ISBN is indeed assigned by the publisher, who has been granted an ISBN prefix by the ISBN Fairy. That's same as DOI.
But DOI feels more like Amazon's book numbering system, their ASIN. That relies on an opaque entity which may well lose track of any particular item, for their own reasons... though ASIN has not been promoted as a standard index.
978-0782120813
I had no trouble finding the book via this magic number. I don't know how that compares to a 25 year old DOI for an item that was in limited publication.
(shameless plug, fair, but it's an example for which I happen to know the provenance of the isbn, even before publication, and I also have an idea at how obscure this item turned out to be after public distribution.)
DOI Content Negotiation to retrieve metadata in a way that's interoperable between DOI registration agencies: https://citation.crosscite.org/docs.html
Crossref is expressly not opaque. Although we have a legacy codebase, we've committed to fully open source and open data.
https://www.crossref.org/blog/crossrefs-board-votes-to-adopt...
(Disclaimer - I'm at Crossref)