Why haven't they built a native UI toolkit for JS, though? What will WebAssembly give them that makes it worthwhile?
If WebAssembly does a good job of exposing features needed for high-performance code, it could become feasible to move everything to WebAssembly and ditch support for native code on both platforms.
Edit: I should clarify that for certain types of apps WebAssembly might be relevant but the discussion seemed to be out UI layer and I don't understand how WebAssembly fills a gap that a native API in JS could also provide along with the same challenges.
A good example is games. Some do manage to use Java, but it's mostly a hindrance; being able to compile languages with a C style ontology to a platform-independent and efficient VM would be very helpful here.