Mobile devices are here to stay, and have already surpassed desktop workstations in number. However both serve entirely different purposes and the distinction between both is blurring more and more as devices such as tablets and foldable laptops become popular.
The question is, what activities are best served by either a phone or a desktop computer? It's easy to see that both will continue to each serve a purpose.
What I do believe is that the Web will be less and less relevant as time passes, and as information is disseminated in different formats. This is particularly true for mobile devices. The webapps of yore, in phones, are replaced by standalone "Apps" you can download from the vendors' (iOS, Google) stores. Google, Wikipedia, Tumblr. I believe this is to become the "Web 3.0" (good riddance to javascript and bloated ass web browsers).
As for desktop-specific applications, the same has been true already for decades, for the software that people use for work (be it spreadsheets, audio/video/image editing or CAD applications) have been delivered as standalone applications (indeed, there was no other way before html5+javascript) ever since their conception. The proliferation of web-based applications is just a consequence of the "Web 2.0" hype and even those are considered to be less performant than their binary counterparts.
What I am trying to say is that new services will emphasize the web less and concentrate more on providing their own frontend in the form of a binary application over which a vendor has better control, and hopefully, the web browser will eventually be nothing but a memory, and a lesson for future developers as to what happens when you start bloating a single application to provide all sorts of contents possible.
Another way of saying this is that, with the growing dependence of everybody on networks, the OS itself is mostly reduced to be a web browser in itself, with standalone applications taking the place of old webapps.
People are starting to detract from javascript, either by blocking it altogether, transpiling from other languages (Elm, clojurescript, and myriad others), and proposing stuff such as ASM.js (which if you think about it, is far less efficient than, say, android bytecode, with pretty much the same development cycle).
I for once am happy, for soon we might do altogether without disgusting web browsers.