boost VS website-v2-docs

We do not control boost.org, and putting this on a subdomain imputes an authority for decision-making we don't have. Building it on some temporary domains, then presenting it as a choice is the only approach compatible with Boost values.

Not at all. There is no "they", the Boost Libraries is just a collection of individual libraries that each have their own author or maintainer, usually unpaid (although the C++ Alliance has changed that somewhat). The only funding that "Boost" gets is from running the C++Now conference, and some of that pays for the hosting of boost.org.

Though the links within it seem to be to boost.org and therefore fail to be resolved. Well I can manually replace them with https://www.boostcpp.org/ like:

Oh wow, it behaves incorrectly...when I visit http://boost.org/ or https://... it shows spam on my side, whereas when I visit https://www.boost.org/ it works as expected.

If you wondered why Boost headers look like hell that's because once your library ends up being popular, you're kinda stuck supporting quirky compilers -- either yourself, or accepting patches for it.