Rather than a new web standard or ignoring "legacy", I'd point out that there are even web browsers for the Commodore 64 and Apple II. You don't need to implement every tag, the point of HTML is to ignore tags you don't understand and it should still render. Pages with correct markup are still readable in ancient browsers that don't understand CSS. If your page isn't readable in Lynx and Links, you didn't code it properly.
You can't support every site obviously, but Links [3] has shown you can go a long way by just supporting a subset of web features. The speed when you're not trying to render pixel perfect layouts is astonishing.
[1] http://www.jaruzel.com/gopher/gopher-client-browser-for-wind...
IMHO it could help a lot if a browser could let you configure the way it treat a particular unknown tag: just ignore it with its entire content or treat it like another kind of tag it knows.
Lynx/Links could really use an update (excuse me if they already have it - they didn't the last time I checked). There is nothing hard nor improper in supporting/using most of the HTML5 semantic tags.
Another thought: what if browsers develop the ability to render markdown natively (in addition to HTML)?
But indeed I'd love Markdown or something like that (AFAIK AsciiDoc is better) to be everywhere.
I actually evangelize Markdown on daily basis encouraging everybody to use Typora instead of MS/Libre Office in every case when there is no practical reason to use the latter.
Yes, I bloody do!
And by the way there is a less radical alternative option: just give up support for all the legacy features, quirks and redundancies - perhaps this might simplify the code significantly already.
Another fact to keep in mind: there already are Gemini and Gopher.