You don't! I switched to using links on the linux framebuffer and it rocks. Yea, there are a few sites that I have to pop over to X and Firefox, but for the vast majority of web sites that I visit, including this one, it works like a charm.
And it's lighting fast. Trully stunning. 10-20ms to render on a circa 2008 thinkpad.
And it's pretty good straight C, and very hackable, and only around 70,000 LOC. First thing I did was join it with guile and write a bit of glue code and I'm now adding features to it faster than you could git clone firefox, let alone begin to read its code.
I mean, modern websites do a lot more than display documents. They're certainly bloated, but they increasingly need to "do everything." Normal people do so much of their computer usage in the browser that it could probably _be_ the operating system and most people wouldn't lose any functionality (see: ChromeOS).