First, I suppose I'm obligated to say that I'm a huge fan of Wasm (and was a huge fan of pnacl for years before that).
Wasm (like asm.js before it) is target at unmanaged languages. A C++ codebase likely does very well with good performance. That was not what I was talking about. Convincing a game company to write their games in C++ is trivial. Convincing that same game company to write their normal CRUD website in C++ would be incredibly difficult.
Looking at apps, there's still issues. Consider Qt. While it's very possible to write everything in C++, loads of companies jumped straight onto the QML/JS bandwagon because its (generally speaking) much faster to write safe code in JS (also, running the v8 version that Qt requires would be terribly slow compared to the native engine). UI development is hard no matter what and C++ doesn't do it any favors. JS features like closures and dynamic objects make many things easier than static classes functions.
This means we need to look away from C++ to something that is managed and has faster code turnaround times. The best possible languages for this are (IMO) Scheme (or maybe Common Lisp) and SML (or maybe Ocaml or F#). You could also make arguments for something in the vein of Dart or Kotlin.
How do you bring these languages to wasm? If you use a JIT, you run into a rather large payload (4-10mb of code is going to have obvious impacts). In some cases like Ocaml where a native compiler to wasm is in the works, you still have a GC issue (basically, you can make an advanced GC that is slow or a basic GC that is "fast", but with other issues).
The addition of DOM API will solve the GUI issues (and maybe they'll rework them to be more like dart's API). Adding hooks into the builtin GC would reduce payload size down to something closer to unmanaged languages. 10 years after those are added (when outdated browsers can finally be ignored), wasm will finally be ready to replace JS.
Adding those features doesn't seem to be highest priority. Unfortunately, you and I will probably be nearing retirement age before they are generally usable.
As a point of interest, JS code could be getting much smaller and much faster to parse (plus becoming a better compilation target) with the JS binary AST proposal.
https://github.com/binast/ecmascript-binary-ast