In my opinion, WebAssembly just needs to be better than what it replaced (asm.js) to be called a success story. And it definitely is better than asm.js.
Unlike HTML or CSS or JavaScript which are by definition large enabling technologies that enable completely new things, WASM is always that small step to make C/C++ and other native languages usable on the web. I never thought of WASM as a magic wand that makes web apps super fast and you probably shouldn’t.