What do you mean with "don't inherit anything"? Using the existing binary ABI is mandatory for interoperability so yes, in that sense every new programming language inherits something. Other than that, there's plenty of languages that have fully self-contained toolchains and runtimes, e.g. Erlang and Rust come to mind. Guix bootstraps its entire environment from a minimal Lisp implementation. There's also Microsoft's CLR and its entire ecosystem of programming languages, but I don't know if the runtime exists next to the Win64 C/C++ base or on top of it.

HTML is entirely the wrong comparison as it's a document format and not a programming language, and "as long as you can write a browser" is not a simple condition. Do we have any browser (even in development) that isn't written with current toolchains? Or a headless javascript runtime perhaps?

HTML as the "transport"/"dialect" to keep compatibility with the existing computational world. What I mean is from the ground up, no C, no erlang (which Im a big fan of in terms of application organisation), no Rust, no Javascript. Start from first principles, OS'es closer to uni-kernels, sane sharing/privacy policies, ability for instance to start an "executable" (already an abstraction tied to the current mode of software production, albeit a perhaps useful one) with a narrow set of scoped access. Then it only has to implement a browser/subset of it to parse HTML and it can "access" most of the relevant parts of the existing software world (internet). Ditch anything complex, if necessary make a browser that just uses flexbox, no other things, no backwards, compatibility, if you need compatibility buy a normal laptop with a normal OS, that comes with all the cruft, but design this new one from the ground up.

But I also don't understand why (without compatibility layers) a browser should be as complex, or remotely as complex, as currently, specially with all the knowledge in hindsight.

I'm not saying this is easy, doable, or whatever, but that was what I meant.