A hard disagree on most of this, from someone who used to be strongly in the anti-PDF camp, for all the reasons Jakob Nielsen has argued for decades.

What changed my mind was tablets, and a large-format e-ink tablet specifically: 13.3 diagonal inches, roughly the size of an A-4 sheet of paper, with 1650 x 220 pixels at 207 ppi and 16 greyscale shades. It's an absolute game-changer. <https://onyxboox.com/boox_maxlumi>

The biggest problems with PDFs are computer displays and content management tools. I'm severely disappointed with the on-device capabilities for managing a large collection (1,000s) of documents. I'll also admit that many people won't have such concerns, the point remains that for those who do, it's a serious pain point.

The tablet solves the first issue, though the second remains a major irritation.

PDFs are a reasonable choice for many informational contexts, especially where the content is stable over time. Books, manuals, reports, brochures, and the like.

Of the points made in the article (which is ... actually an advertisement for a specific HTML formatting system):

Item 1: PDFs are painful to read on phones. Well, yes, everything is painful to read on phones, PDFs only slightly more so. The issue isn't PDFs, but the inappropriate size and form-factor of phones. (And you've noticed how they keep getting larger over the years, right?)

A smartphone is a compromise in many directions, and is generally a quick-reference tool, not a dedicated reading or research device. The display size is about that of an index card or product label, and it's best suited to content of roughly similar scale.

What a PDF offers when coupled with an appropriate display is paginated content, sensible margins, high-quality typography, deliberate (rather than incidental) layout, and often options for bookmarking and annotating specific document contents.

Items 2 & 3 (accessibility and search-engine optimisation) both depend heavily on intent, creation tools, and context. PDFs can be accessible, much as Web pages can be, though many of both fail abysmally. Accessible design is its own specialisation. Ironically, of course, simple versions of both PDFs and websites tend to have good basic accessibility. SEO optimisation is typically addressing PDFs from the wrong accessibility angle: materials best suited to PDF formats should have and be discoverable by metadata: title, author, publication date, subject or topic, and the like. SEO relies on internal descriptions of a document as well as relevance and reputation of the hosting site itself. For material published as PDFs, the authority comes from the author and/or publisher principally, as well as external references (citations, reviews, references).

For item 4 I'll call on Goodhart's Law: analytics-driven content generation is much of what's wrong with the present Internet.

Item 5 has two easy counterpoints: the worst Web content is far uglier, and less useful, than even a middle-of-the-road PDF. Beauty in publication matters far less than the actual content, and over-designed content (such as the several examples shown in the article) actually provide less information than many pedestrian formats and styles. The best books are exceedingly conservative in their design. In my experience, even middle-of-the-road websites send me running for the Reader View mode, and the worst are utterly unredeemable. (Though often dumping plain text to an editor and removing cruft can make extracting critical information possible.) I'd point to Hacker News as a plain-but-valuable Web design ... and then note that I restyle even it with a set of CSS hacks linked in my profile here.

PDFs aren't principally designed for presenting images, though there are catalogues and the like which I find more useful than, say, many online shopping websites. In particular, many people don't realise that PDFs are in fact potentially fully interactive, and could, if specified, provide expanded views of graphics, or interactive charts and the like. As with most such capabilities, the power is very often abused, of course.

Of the final three points, 7, 8, & 9: for third-party tool integration to be so useful, painfully few examples and benefits are given. In fact, PDFs are a key format used by document management systems such as Calibre and Zotero, which is the key third-party tool I'd want interacting with my PDFs. Phasing out of PDFs has some legitimacy where information is principally consumed online and briefly. Yes, far too many organisations publish information only in PDF format, itself often cumbersome, and one suspects specifically to increase frictions of accessing information. This is a user intent and not an intrinsic failing of PDFs. "Plenty of inspiration" is ... vacuous.

And I'll note: there are other document formats, most notably ePub, which closely approach PDF in overall suitability to text, whilst remaining sufficiently fluid to be readable across a staggering range of display sizes and capabilities. If you're publishing substantial and reasonably static documents and want to provide access for smartphone and tablet users, this is an excellent choice. I still prefer PDF or DJVU (another static format) for reading books as these preserve page references and (when based on original published formats) the design of the original document, but ePub is still usable, strongly preferable to HTML-based Web documents, and more than adequate in most instances.