LLVM kinda proved having a common target back-end doesn't kill language diversity, it actually achieves the opposite.
The way that coding language and deployment/executable language have been tied together (JS for both) has served as a force that pushed everyone toward that single language.
Now that WebAssembly promises to remove that force, will it be a free-for-all, or will other forces push toward standardization on a few languages? And if so, what will those forces be?
To be even more specific, in the early days now, the main allure of wasm is performance. So the focus will be on languages and toolchains capable of generating optimized native code. Out of those, look at which ones are easy for the developer to set up (both in general, and for wasm) on all popular developer OSes.
So, I'd say that Rust will probably be the biggest beneficiary.
I imagine binary size would be a concern for web development, what is a negative for complex runtimes... But then, if I carefully set the compiler to trim dead code, my Haskell email server is smaller than any modern JS framework (still larger than a new version Jquery), so the runtime may not actually make much of a difference.