Two big reasons: bundle size - few hundred KB uncompressed vs multiple MB already compressed with WASM. And the DOM lives in the JS world - WASM can't touch it directly and has to cross the JS bridge with serialization overhead every time.
On top of that, since the browser platform has different characteristics, you can surgically drop down to native JS functions instead of compiling and bundling everything. For example, things like Unicode code point databases are already built into the browser - no need to ship them in your bundle when you can just call into the native APIs. The compiled output is also readable which helps with debugging.
For web apps generally JS is the better target IMO - you want the smallest possible bundle and the app reacting as quickly as possible on load.