This is exactly what I was thinking, the most advanced LaTeX typesetter is proba...

This is exactly what I was thinking, the most advanced LaTeX typesetter is probably mathjax, but it can't and probably won't [1] handle full LaTeX. Just consider this pretty simple LaTeX,

  \begin{align}
    x &= 2^2
    \intertext{so we can simplify}
      &= 4
  \end{align}

With a little bit of fanciness (sourcing the .sty sheets) behind the scenes, this could faithfully reproduce LaTeX.

[1] https://github.com/mathjax/MathJax/issues/736

Edit: formatting