PDF is for printing and for (well, with the exception of a few edge cases) guaranteeing a layout and display given a set of paper dimensions. HTML has the advantage of responsiveness, but the inherent problem of variable output.
When I was a professor and advising my students on creating portfolios, I told them to build websites of course. But I told them to also have a link to a one-page PDF because many organizations (not just academia) forward resumes within an organization to someone senior who eventually prints it out. And you don't want that person's first impression be whatever your website's print.css churns out.
Variable output is not a problem, it's exactly what's needed. The days of standard paper formats are over, old man: in a decade people will have documents delivered straight to their retinas, or read into their ears—but everyone will still have to scroll PDFs back and forth with no possibility of reformatting, because lots of papers are published in it.
If you want to have your document printed nicely, just prepare it for printing along with other methods of output. The best way to do it is to not use some crazy layout: have a single column with images between paragraphs, and your documents will look fine on any device. All problems of reformatting documents stem from the rigid two-dimensional layout mentality, while the flexible approach requires stepping back to the one-dimensional semantic flow.
(Actually, standard paper formats were never around, because—surprise—my country doesn't use US paper formats.)
No, variable output is not "exactly what's needed". Layout of information is an actual skill -- whether it's a resume, a newspaper front page, or a photo gallery -- and we can expect layout to be an important design factor as long as humans have eyes that can process information in formats other than a byte stream.
HTML has been an excellent format for delivering data and information across innumerable devices and visual dimensions. That adaptability comes with tradeoffs. As others have pointed out, anyone who's browsed the Internet Archive knows how HTML, beautiful and organized in its own time, can look like slop today. Paper/PDF's tradeoff, of course, is its rigidity.
When I was a professor and advising my students on creating portfolios, I told them to build websites of course. But I told them to also have a link to a one-page PDF because many organizations (not just academia) forward resumes within an organization to someone senior who eventually prints it out. And you don't want that person's first impression be whatever your website's print.css churns out.