Apple still control what API you can use in their mobile browser, and it's not like they are at the forefront when it comes to implementing Web API today, especially when they also forbid any alternative browser on IOS. Ultimately WebAssembly is limited by the API it has access to in the context of the browser (and the resources that are granted by the browser). All the promises of the "web as an app platform" have not been fulfilled yet.
IMHO WebAssembly will play a bigger role on the server, with nodejs for instance as it will allow portable native code distribution.