The final dream is having a unified, Desktop, Consoles (Ps4 and Switch) and Browser runtime with a unified API (where sensible). One can dream.
With the browser, you're just adding another abstraction layer that has even more complexity. WebGL is far for a decent spec. And we're talking just graphics, as I mentioned before, audio and networking have tons of unstable and untested code.
Multimedia programming is already hard on native environments. I don't see the web being a friendly environment anytime soon. There's no silver bullet, "code once, run anywhere" for games and multimedia.
> An important constraint is that, while WebAssembly should allow tight integration with the Web, it should not bake in details or Web standards dependencies that prevent execution in a non-Web embedding. This suggests a design (called opaque reference types below) that hides the details of JavaScript and WebIDL behind Web-embedding-specific builtin modules. On the other hand, WebAssembly can define a set of native GC primitives that allowed portable GC code to be written regardless of the host environment.