The performance of touching the DOM and browser APIs will be the factor that decides that, imo. I think you may be underestimating how many people are partially or heavily disgruntled at javascript, and would happily replace it if given the chance.
If speed is not an issue, and it's purely by choice of the user, i think there will be a lot of interesting changes to the web in the coming years.
Hell, for many applications i'd even be willing to accept a speed loss to use "my preferred language". And, in the event that certain tasks are indeed too slow, perhaps i'll be able to pass data back and forth between my WASM and JS to let JS deal with the performance critical DOM.
Regardless, i'm quite excited, and hope to see something fruitful from it.
It's not actually the nightmare many make it out to be with ES6. I actually enjoy writing it quite a bit (I have mainly a functional background)
On the web it's.. well, just JS. Some languages that transpile to JS.. but ultimately they're all pretty much just JS.
I think the community of people who want tyoe safe languages is large, and this will the a target for them.
I just hope for Dom bindings through the WASM ABI.
Writing glue code sucks.
Define an ABI for interacting with the DOM. And allow WASM compilers to target it.
At the very least JavaScript will always be around as a "glue" language to use wasm binaries.
I think of the relationship between JavaScript and WebAssembly as the relationship between Python and C. JavaScript will call out to a wasm binary for some "heavy lifting" and JavaScript will be used to "glue" the data to the DOM. Also like the Python-C relationship, the wasm can be a compile target for non-javascript libraries.
But I honestly don't see writing non-javascript web applications being mainstream any more than it is now at any point in the near-ish future. It's possible (both now and in the future), but it's always going to be a leaky abstraction, or your language will end up being similar enough to javascript that targeting wasm is largely pointless (think TypeScript or Flow).