Transpilation to JS always sucks. JS was not designed as a compiler target. The point of WASM is exactly that: Compile any language on the web without getting into the JS limitation.
Performance. WebAssembly has no JIT stage, it gets AOT compiled straight to machine code. Plus, it gives (or will give) much lower-level access to features like threads and memory allocation.
Thanks to Spectre I don't think we'll be seeing threads anytime soon. Well, not threads with shared memory anyway which removes a lot of the point of them. Same reason JavaScript just lost SharedArrayBuffer, too easy to make a high precision timer out of it.
You're describing asm.js which had significant issues as a compilation target. The generated javascript code was massive and it took several seconds just to parse it.
Right now, some of the biggest users are applications where JavaScript's garbage collection pauses are show-stoppers, like games and audio recording software.