I have been making websites in one way or another since 1998.
These days-- about 20 years later-- when I set out to make a webpage, I make sure it at least renders comprehensibly, if not with the full intended appearance, in Lynx, as well as Links' text and graphical modes.
No sanctimonious reason. I don't think I'm saving the web. I don't think I'm making my sites any more accessible to the blind. They are nice bonuses, to be sure. I hope it helps someone.
I am simply prone to two things: distrust of the new, and decision fatigue. In other words, I'm helpless against the ravages of overthinking, overdesign, and nostalgia. Most artists work better in extreme limitations. I am one of them. No argument.
I also have among a handful of persistent creative patterns: make what I want to see.
There is a sort of sanctimonious side to it, albeit marinated in nostalgia in its own way. >
I also see it as a social issue. Broadband isn't as ubiquitous as some people (mostly in the first world) seem to think it is. If the internet had been as asset-heavy and latency-dependent in the 2000s as it is now, I would have been hopelessly isolated on my connection; even when I had broadband (satellite), it was capped at 160Mb per hour. A single web page these days can easily weigh 5Mb.
(Mine is, of course, no exception-- disable CSS, and images, though, and everything will still work.)
Universally consistent internet speed also seems to be the first line of defense that net neutrality in the US is falling back from; I have no confidence that my website(s) will remain on solid footing.
I will write my websites by hand, and they will work in text mode browsers, at least where there is text to be read. Because raw text has been around over half a century, a geological timespan in computer science terms, and shows no sign of going anywhere-- and automation and convenience hold no immediate benefit to me over that. Do I necessarily think my work is worth preserving? I don't know. But I can certainly litter the waves with 'I told you so' later on.
December 2017 ... come back in a few years and see how this has held up.