It should be totally possible. You should be able to fetch the HTML, process it (as Reliability seems to do) and define your own render logic in an A-Frame component.
You answered your own question. I'm more excited about your approach of alternative ways to render existing Web content over a DOM to texture API. VR is an exciting space to experiment.
I understand that viewpoint but I think the WebVR will be isolating(the normal web doesn't work) and lack uptake until, for example, github.com can be used directly within VR.
I don't believe github themselves will make a native client any time soon, and we shouldn't expect any other websites either.
I totally agree. We will be pursuing both approaches. HTMLTexture requires consensus and coordination with other browser vendors to come up with a sensible standard and it will take a bit of time. Alternative ways to render page information using WebGL can be explored today.
Yeah, I think so? Like parse the HTML and present it in a nice way in VR? That might be interesting for us to show VR content stand-in for non-VR sites (like Wikipedia) from our browser.