I am not convinced about that for two reasons:
1. Good money has been invested into making JS fast. If you look at actual benchmarks it is currently quite easy to end up in a situation were your WASM-based solutions might perform WORSE. So at least for now the performance advantages are not that great to begin with.
2. On the frontend, you still need JS to use the DOM. Getting data back and forth from JS to WASM can become a bottleneck. Plus rare processing speed is rarely an issue on the frontend and IO-bound stuff is something JS is already good at.
If you don't do frontend stuff, you don't have to use WASM, you know? You could just go native binary in the first place especially as modern languages have great cross-compilation support. (Edit: If you are after performance mainly and don't care about sandboxing and other advantages.)
Yes, if you need to do some image processing on the frontend or want your users to mine crypto for you, yes WASM has already uses but generally I am a bit skeptical.
Now WASM is awesome for getting you the C/C++/Rust world in the browser, sure. The performance improvements might be overrated though considering the additional development costs compared to just using JS.
(That was more a dig at the WASM hype in general, of course. Not meant to throw any specific shade at AssemblyScript. Still an interesting project regardless.)