DOM manipulation is going to be available at the WASM level in the future but it's going to be inefficient to do so just as it is inefficient to do image processing in JS right now. The only difference is that JS is the only viable option now if you want to do image processing on the web. WASM exists to solve this problem and complement JS. Hell, look at WASM's and JS's logo. They're two puzzle pieces that fit together.

Your analogy doesn't sound right to me- there's nothing about wasm that would make it slow to manipulate the DOM, while there is plenty about Javascript that makes it slow to process images.

Manipulating the DOM from wasm shouldn't be any slower than Javascript. Slow in general because of the DOM, perhaps, but not because of wasm.