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.
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.