As long as GPU support is not functional in headless, "any web page" is a misnomer. A large enough percentage of sites use GPU acceleration so that headless mode is useless. This needs to be addressed by the Chrome team.
What do you mean "use GPU acceleration"? Are you saying that a large percentage of sites use WebGL? Using GPU acceleration for web page rendering is just a browser performance optimization. They can render the same page without GPU only slower.
I'm more specifically talking about WebGL. We'd love to use headless chrome at our company but we can't. But even for things like CSS transforms, we do a lot of really heavy 3D work and software emulation won't cut it.
CSS transforms work just fine without the GPU. We use it extensively for screenshot testing our CSS transform-based animations on https://oddslingers.com.
No, I'm not. We are using both a webgl context to render 3d objects on the screen using shaders, and 3D CSS transforms to render overlays on a video stream.