Actually many of us use es6 with a compiler to turn into some dialect of js that runs in browsers. We will hardly notice if our code starts getting compiled to wasm instead..
But yes, that's the future I'd like to see. Browsers only have a WASM engine, and provide a JS->WASM compiler client-side for backwards compatibility.
Obviously if we're trying to run a full JVM or CLR in WebAssembly, that will cause problems, but C# and F# both have compile-to-js targets that would likely just get faster.
You'll need most of a runtime anyway, since it provides much more than GC.