Eh, there isn't any reason that it couldn't at some point in the future. That won't be happening any time soon, but I'd love to see that day, personally.
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.
You'll need most of a runtime anyway, since it provides much more than GC.
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.