Because I've read it here and elsewhere quite often: What is missing from WASM in the browser isn't "just" DOM access, but "everything" else - including fetch or XMLHttpRequest - too. Here is a list of all web APIs supported by browsers and not supported by WASM, the DOM is just one of them: https://developer.mozilla.org/en-US/docs/Web/API

But at least there is hope, that these interfaces will be available once GC is final and supported by browsers:

    Once GC is supported, WebAssembly code would be able to reference and access JavaScript, DOM, and general WebIDL-defined objects.

Last paragraph at https://webassembly.org/docs/web/