If wasm becomes good enough to replace JS, it will not be rust. It will be easier to use languages like C#.
The DOM has it's own lifetime decisions, but lifetimes are the most central concern for Rust. I don't think both can be conciliated without a major rewrite of one of those parts.
I find Rust more pleasant to use than C#. If you had said F#, I woud be like "maybe" but not C#.