I think that would be really neat for small scale web publishing, but making it a subset of browser standards could be a really difficult sell to the people making browsers. While it's easier to build a browser to a subset of such a massive set of specs, the subset will drift towards a "similar but slightly incompatible standard" pretty soon after it's decided on. Following the development of Ladybird has given me an appreciation for just how often the "spec" for the web changes. (in small ways, daily.) That locks new browser implementations into a diverging standards track that would be very difficult to get off of.
I think something like a reference implementation (Ladybird, Servo or even Vaev maybe?) getting picked up as the small-web living standard feels like the best bet for me since that still lets browser projects get the big-time funding for making the big-web work in their browser too. "It's got to look good in Ladybird/Vaev/etc".
An idea: a web authoring tool built around libweb from Ladybird! (Or any other new web implementation that's easily embeddable) The implied standard-ness of whatever goes in that slot would just come for free. (Given enough people are using it!)