Right now. WASM has been supported by every browser for a while now, and most webapps are made with WASM. That said, it's not a replacement for Javascript, most people only use it on things that need to be high performance like heavier apps and web games. Nobody really makes websites that rely on WebAssembly instead of JS to my knowledge.
From my understanding, it’s because WASM is pure (deterministic) and needs stateful entry points in order to work. For this reason, a JavaScript bit to interact with it is a requirement at the moment.
While it’s true you can’t do it in WASM directly, there are frameworks that interoperate between WASM and JS, such as Yew
One only needs to create an interface between them, since WASM is capable of calling JS functions. DOM manipulation then becomes as simple as calling a function in your language of choice, such as with web-sys
JS is slow, but I program Rust and Scala. Every internal app at my company is react based and I spend most my time waiting for that bloated framework to load a simple table. It can take seconds to load a 20 route paginated table from source.
We've got a WebAssembly web-UI at $DAYJOB. Implementation language is Rust, we use the Leptos framework (although other mature frameworks are available for Rust).
Pros:
Same language and similar tooling as in the backend. Most libraries work the same way (obviously excluding libraries that read from the filesystem, for example). This is especially good, if you've got lots of "full stack" devs.
Same model classes as in the backend. If you change a field, the compiler will force you to fix it on both sides. It is compile-time guaranteed that backend and frontend are compatible.
Rust is a nicer language than JS/TS. I find especially Rust's error handling via Result and Option types + pattern-matching works really well for UI stuff. You just hand the Result value over to your rendering stack and that displays either the value or the error. No unset/null variables, no separate error variable, no ternaries.
Having a strict compiler makes it less bad when you're lax on testing, and frontend code is a pain to test.
Cons:
If you've got pure frontend folks, or people who are deep into React or Angular or whatever, those are not going to be as productive.
The JS ecosystem is massive, you just won't find as many component libraries for Rust, which can definitely also reduce productivity.
With me being in a team with few frontend folks, I would definitely opt for it again.