Running anything with the GPU introduces a huge amount of latency, it only makes sense when you need high throughput and have large enough workloads to justify the latency. SIMD code can be interleaved with normal native code with zero latency.

And then there's the fact that WebGL is so much behind the state of the art that it's not even funny. Sticking to an old version of GL/GLSL severely limits what you can do with it.