Well they don't really. What ought to happen is someone just makes a new browser (or adds support in an existing browser) unilaterally on an experimental basis. If it's good enough I imagine it would catch on. The limiting factor is presumably that that's a lot of investment for an experiment, but getting anyone else on board without a successful experiment is going to be impossible. (well, also, you have to have a good enough plan to be worth switching. I don't think dart/flutter was that.)
A nice starting place would be if one of the major browsers added an easy to use extension point for swapping out languages. (at least I'm not aware of this existing, nor that I've looked)