Plus first class DOM support for wasm is coming at some point in the future, so I'd imagine any properly supported library could implement it once it is finalized.
I'm not sure I want this. I use WASM as a compilation target, but I rally enjoy the simplicity of the platform and how all connections from and to the Javascript world have to be explicit. Allowing more transparent access to the DOM would diminish this highly defined interface.
Wasm is specified in two layers; wasm itself and then the api the host provides. All of the "external surface" stuff is in the host, not in wasm itself, so wasm for another host doesn't get larger.