You can already do this. You don't need a special browser. This approach always sounds great until you consider how native input, text selection, copy-paste, etc. behave on mobile. Not to mention accessibility, screen readers, and so on.
The design behind WASM helps keep this iteration of Macromedia/Flash/Java/ActiveX stay quite secure, at least until people start adding the extra APIs that a certain subset of WASM enthusiasts trying to turn WASM into another JVM are going for.