Emscripten and experimental backends hardly count as support for Nim. Python can run in webassembly by the same token, but no one would. The standard rust compiler compiles directly to webassembly, natively, with the stable toolchain.
In other languages, yes, the js bridge is a problem. However, not only will this be fixed in browsers at some point, but rust is so fast that TODAY yew.rs, a mature wasm framework, is faster than react.
My thoughts are better explained in this video https://youtu.be/P4LMfkFLRsI
