There have actually been some "demos" in the demoscene, submitted to parties and everything, that were written for the browser. Mozilla jumped on this and is sponsoring two compos (competition categories) for this year's @party: Best Single Effect and Best Multiple Effect demo in a web browser. http://atparty-demoscene.net/compos.html
No Linux OpenGL driver I've ever seen was in any fit state to be exposed to the public internet, for reasons of both security and stability. Last I tried developing GLSL shaders on Linux, a non-terminating shader would hang the entire system and only a hard power cycle could recover it. And nine out of ten times, the non-terminating code was the compiler's fault and not mine.
If we need special cooperation from driver developers just to make WebGL safe on Windows then Linux is not going to have it for a long, long time. This is yet another reason that WebGL makes a bad standard.
I would imagine it's due to driver support on Linux. A lot of the open drivers still have issues with 3D acceleration (nouveau for instance). By disabling acceleration in the browser, they minimize unnecessary bug reports and user complaints. Most linux users are competent enough to enable it if they desire.
I'm on Archlinux using an old and dusty Nvidia card and I have never had any problems with WebGL so far. In fact, when I often share WebGL links with others they complain about it bringing their computers to a crawl, and they're generally using a non linux OS. Mind you, things are probably drastically different for the poor souls who have to deal with ATI on linux. But in those cases, I'd say the problem is with ATI and not WebGL.
Only the NVidia binary driver appears to be stable enough to run WebGL on Linux. I believe Firefox and Chrome disable all other ones by default, and even older versions of NVidia's.