An example of that is drawing a DIV and applying a CSS 3D Transform to it. By doing so you'll modify it's display on the screen so you'll need to recompute it's actual bounding box. If you compute the BBox on the GPU and never access it anywhere else, everything is fine but as soon as you have to use it in JS you're screwed because you'll have to transfer data from your GPU to your RAM. Doing so at 60fps is very expensive, then you'll take a performance hit from JavaScript being usually slower than C/C++.
That's not the only problem you'll have, text rendering is probably the biggest one. As you might know, textures are rendered using memory friendly algorithms. To ensure maximum readability and quality you'll have to (1) use a lot of memory and / or (2) apply some advanced filtering so your texture doesn't lose quality. Those techniques are quite hard to implement if you're not a 3D programmer (just check what happens if you try to rotate text in CSS and select it) but more importantly you'll find yourself reinventing the wheel.
In the end the only difference you'll have compared to the real browser renderer is that you do less computations from CG(GL) to RAM (JS), hence the performance.
You can check this very old project of mine where we tried to link DOM and WebGL Nodes: https://github.com/aout/SAGE
edit: just saw the repo wasn't entirely up to date. Done now.