How does handing in an essay on paper 'fight the power'? Paper is just as corrupted as the Web. Anecdote: a couple of years ago, before a long coach journey, I decided to buy a pen and paper so I could pass the time writing, drawing, mathematical playing, etc. In the centre of a large city (Birmingham, UK) it took me about half an hour to find anywhere which sold blank paper rather than pre-printed magazines/newspapers/books/etc. (I eventually found some in Poundland; an underrated shop IMHO). I nearly missed the coach.
Rejecting technologies, like email, is self-flagellation. Whether a teacher can or can't force a student to have an email address is irrelevant; all that's needed is to SMTP the server with a syntactically-valid FROM address, like "email@example.com". There is no requirement for that address to even resolve, let alone for it to accept mail and make it available to you. So what if you get marked as spam, that's always a hazard even from established providers.
Likewise, if someone wants to make something available to you via email, there's nothing stopping the use of a one-time-only address, e.g. mailinator.com or something similar with a password, that disappears after 24 hours.
To refuse email in such a way is like refusing to write English in left-to-right order; or using a fountain pen full of invisible ink: it's petty and silly, which is fine if that's your intention, but as a serious statement it achieves nothing.
In contrast, refusing control by "The Corporation" is definitely a Good Thing (TM). It's why I've never used Facebook, Bebo, or any of those other register-to-view silos and never will. It's why I deleted my Twitter account after their chilling meeting with the UK government after the 2011 riots. It's why I host my own blog, Git repos and anything else I would miss if it were deleted. It's why I use only FOSS software, on machines which require no driver blobs or proprietary BIOS (except for the GSM driver on my OpenMoko; I'd be glad to hear of any alternatives). It's why I download videos from YouTube, iPlayer, etc. to watch in the ways that I want to (which may be several decades after those services collapse). It's why I use ad blockers, NoScript, hosts file blacklists, etc. It's why I only turn on my smartphone (OpenMoko running Debian) occasionally, when someone asks me to expect a message from them. And so on.
It's often said that technology is neither good nor bad, only its uses are. Ignoring the "bad" uses of technology doesn't require abandoning the technology itself. The article decries "digging up Wikipedia and planting cabbages over it", but there are also many other areas of the Web which aren't "bullying and wheedling and neediness.. invisible selling... loveless flirting and cowardly mocking... unbearable long silences and the ceaseless screaming chatter... vengeful rivalries... frenzied desperation and ...wrenching loneliness.". Does "jacking out" make those things stop? No, it's just ignoring them. So why not just ignore them without "jacking out"?
Did the youth of the 1950s rebel against authority by hammering on harsichords in their stagecoaches? No, they blared the sound of electric guitars, transmitted via radio, from cars. Refusing to conform to the new normal by staying with the old normal isn't being rebellious; being rebellious is using the new to create some unfathomable anithesis of normal. That's what I love about Open Source, on top of the fundamental rights provided by Free Software: the bazaars surrounding the cathedrals. Yes, FOSS gives us LibreOffice to file our tax returns; but it also lets us connect a GPU-backed deep learning library to a 3D-printed robots, via software-defined radio running on openly-programmed FPGAs, so we can.... I don't know, because it's so new!
When studying Physics as an undergraduate, our lab sessions gave training on how to analyse experimental results using Microsoft Excel. I refused to participate, claiming that the scientific process should not be beholden to the unknown inner workings of a proprietary, black-box application with an exclusionary EULA and known bugs. I performed all of the required analysis on the course using Gnumeric and Python instead. Whilst still quite petty, I still believe that was still a far stronger message than not using email from a residence with broadband-connected computers.