Because it is the only thing we have sufficiently sandboxed so that we can actually run it untrusted.
I totally get what you want, but we already have a bunch of X-to-JavaScript compilers that pretty much all deliver the experience of: "It works, but it is a bit gnarly, so why would you use this when you can just write JavaScript". And I don't think WebAssembly is going to change that experience much, mainly because it is a pretty poor VM, seemingly designed around the misconception that a lack of features makes it a good compilation target.
I honestly think we could give compiled languages a much better time on the web with a new intermediate language, but someone has to design it for that purpose rather than cargo cult Assembly similarity.