I think WASM is still in an early phase, we'll probably have to wait for 2020 for it to catch on. It still needs: GC/direct DOM access, threads, and Javascript module integration, in my opinion: https://webassembly.org/docs/future-features/ Plus, even the MVP is only supported globally by 78% of the browsers out there: https://caniuse.com/#search=webassembly
Thing will get very interesting very quickly once WASM 2.0, basically, is created and it support is around 90%. But before that, it's kind of early to declare victory :)
I'd argue that most apps are rather passive when it comes to displaying stuff, don't have to crunch numbers and don't manage a lot of data. So an 80s BASIC engine would be enough for it, if the APIs are done well (or 90s Tcl/Tk).
Games are an entirely different matter, of course. I don't see a lot of stuff in between.
But then that will be completely inaccessible to screen readers and other assistive technologies.
Also, Apple tried going down the web app route long time ago, would be great to see them revisiting this idea in a year or so.