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.