I think "this javascript mess" is largely bourne out of an attempt to mitigate content blocking. asm.js is pretty fast and I am not sure how much improvement wasm will provide, but if given access to more of the low-level environment I am concerned advertisers will implement maliscious code and pop-ups in wasm that is non-trivially blocked.
I am not sure exactly how it can be implemented, but I imagine that compiling and serving a binary file could allow for some maliscious things. My biggest worry is that many content blockers override js and search scripts for keywords and functionality which they muitigate. I could see a binary file executing code which provides pop-ups, advertisements or drm which would be harder to eliminate than it is now.
I am not 100% sure if this is true, but it seems possible.
Serving a binary file is in principle no different than serving a string file. What can be done with WebAssembly today can most likely also be done with asm.js.