I'd say it's already there. See for example the https://pagedjs.org/ project which allows advanced typesetting (including for printing) using web technologies. It is already used in production by at least one book publisher (C&F editions)
As an old hand with PDF-in-browser production, I expected much worse of Paged.js than I found. It's powerful and mostly enjoyable to use! Oh, you end up with a large set of CSS rules, and it is not without bugs and gotchas (failing to specify a bleed rule somewhere at least once in every @page context subtly breaks layout; footnote layout is functional but automatic call numbering isn't always perfect, etc.)
You should definitely not expect to take Paged.js out of the box, slap a theme on it, and go; it comes as a box of parts with a mostly complete machine inside, and if it breaks you get to keep all the pieces. I imagine the publisher who uses it must have some prior interest in web technologies, for example.
Nor is Paged.js remotely as capable or flexible as InDesign or a comparable tool, especially for the deeply rudimentary condition of web typography overall - something even as elaborate a tool as this can't really approach fixing.
But Paged.js is also unlike InDesign in having a much shallower (days vs months) learning curve for folks like us with prior web experience, and however equivocal a review I may now be giving of its technical merits, I do actually like working with Paged.js quite a lot.
In my experience Paged.js is at its best when building to PDF, but then that's always my intermediate format when working to paper, because that's where PDF's inflexibility shines. The source of a book block, everything that builds to that PDF, partakes of all the infelicities of the JS ecosystem. But to remake the book itself again, all I need do to start is print the PDF.
That said, it's a shame that the relevant W3C specs (see https://pagedjs.org/about/) still aren't fully supported by browsers (but perhaps such is the fate of niche features), but with that being the case, I'm infinitely thankful that pagedjs exists as a polyfill.