Fortunately, there are other solutions: transpilers. With a transpiler you can convert a ECMAScript2015 script into an ES5 script so it can be run on all modern browsers. The two transpilers with the most support are Traceur by Google and Babel. You can integrate them in your existing toolchain and use ECMAScript2015 today. And when all your supported browsers finally support ECMAScript2015, you can just drop the transpiler from the toolchain. Many developers are using it successfully today. Be aware that Traceur and in many cases Babel too, need a runtime script which will increase the size of your web pages significantly. When you’re writing for Node.js, you are lucky: you don’t need a transpiler and can already use most of ECMAScript2015.
I can see one place where WebAssembly can succeed: portable applications. Wouldn’t it be great to write an application that runs on Windows, OSX, Linux and maybe even mobile devices? Like the promise of Java without the disadvantages of Java. Of course these applications don’t want an addressbar or back button, so a new type of browser will surface: one with only the viewport. Oh, and since the DOM is now the slowest part and operating system dependent, the interface will be replaced with canvas or even OpenGL. And then only the name WebAssembly reveals it was once meant for the web.