Then you're shipping the entire (or at least large pieces of) language runtime to the client since presumably, you'd need to compile that to WASM as well.
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.