You cannot add "full-type inference" on top of a language with a dynamic type system. You also cannot add such type inference to an object-oriented language, like Scala (it may be possible, but very hard and nobody did it).

     the main benefit is catching errors early

Dynamic typing isn't about not specifying types. Dynamic typing is about creating types at runtime.

This enables certain techniques that are very productive, and totally different from what you would do in a language like Haskell, which does have full-type inference.

I also do not think a static language would work as a client-side in-browser language, simply because of the nature of browsers and the web. Such a language needs runtime introspection and even types created at runtime like air. For in-browser stuff I also prefer eval() over static-typing any day of the week.