As the other comment said, outside the browser WASI is what does IO. As for DOM access in the browser, I doubt they want to reimplement the DOM API, because:

• It's insanely complex. This wouldn't be done within one release, but rather take years to add a substantial amount of APIs.
• No one wants to have to maintain two versions of the DOM API documentation. You'd need to basically translate the entirety of MDN to some WASM API description. And in the end, hardly anyone would read it either way, because they're likely using some wrapper library to interact with the API.
• If you're using such a wrapper library anyways, it hardly matters to most people, whether this library generates JS API calls or some WASM API calls.

I try to stay as far away from JS as possible, and I do not think it's worth developing a WASM DOM API. With a competent framework, you can develop complex web-UIs without ever touching JavaScript, which is good enough for me.