The whole js ecosystem evolved to become a damn good environment to write UIs with, people don't know the massive complexity this environment evolved to solve over decades.
Wasm is not now and will never be a magic "press here to replace JS with a new language" button. But it works really well for bringing systems software into a web environment.
1. Non browser application (lightweight cloud, plugins, sandboxing)
2. Performance kernels (like compiling a game/rendering engine or AI stuff)
3. Compiling js-like applications from other languages (eg blazor wasm and others)
The only case where DOM access would be useful is 3 and even there 90% of the gains are already available from the JS-strings proposal to avoid copying+reencoding.
Direct DOM access is otherwise mostly a red herring
WASM is just an extremely expensive toy for browsers until it supports DOM access.