Why you shouldn't use WebGL
* Performance: This is the big one. In 3D graphics and in particular games performance, both execution speed and memory usage, is everything. You can do some great stuff in WebGL but fitting lots of complex stuff (physics, AI, motion) in 1/60 of a second is hard enough when you can scratch around in ASM if you have to, let alone being constrained to javascript.
The Three.js demos are fantastic examples and a great learning tool. But they do feel to me like 90s demo scene[2] stuff. Working within strict limitations and using all the tricks of the trade to produce more than the sum of its parts.
* Libraries: the leading library Three.js is great and getting better and I enjoy using it. But I have a background in 3D graphics and know my way around 3D and OpenGL. Alternatives such as Unity hold your hand and have larger communities from which to draw help from if you don't know much about 3D.