WASM is tied to existing JavaScript engines and their constraints. For example, WASM doesn't support more efficient control flow because of the design of V8 (and possibly SpiderMonkey):
http://troubles.md/posts/why-do-we-need-the-relooper-algorit...
http://troubles.md/posts/why-do-we-need-the-relooper-algorit...
Given the large amount of code in JS and the number of JS developers, not being able to support a major general purpose language rules out WASM as a cross platform target in my book.