You mean a display engine that works like an HTML renderer, except starting from TeX source instead of HTML source? I think you could get something that mostly works, but it would be a pain and at the end you wouldn't have CSS or javascript, so I don't think browser makers are interested.

For starters, TeX is Turing-complete, and the tokenizer is arbitrarily reprogrammable at runtime.

Browsers already support JavaScript anyway, so why not add another Turing-complete language into the mix? (Not even accounting for CSS technically being Turing-complete, or WASM, or …)

As far as I know the Tex team has been working hard lately on supporting accessible "tagged pdfs". Hopefully one day Tex/Latex output will be accessible by default and conversion to HTML will not be needed.

Okay then, what would stop you rendering TeX to SVG and embedding that?

Edit: Genuine question, not rhetorical - I don't know how well it would work but it sounds like it should.

That would (mostly if not always) work in the sense of reproducing the layout of the pages, but would defeat the purpose of preserving the semantic information present in the TeX file (what is a heading, a reference and to what, a specific math environment, etc.) which is AFAIK already mostly dropped on conversion to PDF by the latex compiler.

Couldn't you write a TeX renderer that emitted HTML (or RST, or Markdown, or whatever) with SVG for the equations?

I think this project is based on LaTeXML (https://math.nist.gov/~BMiller/LaTeXML/) which is exactly that (except for the SVG part)