WebAssembly is still far away from being any sort of default for web development yet (if only because IE11 doesn't support it).
I also wouldn't be surprised if Elm compiled to wasm in the future.
I also wouldn't be surprised if Elm compiled to wasm in the future.
AFAIK it's more about missing stuff like DOM access and GC that stands in the way.
asm.js is different enough that it's just not about adding a seperate asmjs "compatibility" target. On the top of my head you don't have 64-bit ints or floats and I believe the way you call asm.js fns from/to JS is different from wasm. Adding asm.js support just for IE 11 wouldn't be worth the effort.