Static types and unit tests don't solve or catch all problems. I'm thinking about event-driven messaging systems, which is pretty common in js; Static typing will not be of any help in that situation.

Sufficiently advanced type systems can enforce an enormous range of constraints. You can for example create a type for trees enforcing that the tree must be balanced; code that would unbalance a tree will just not compile.

You can use a different observer pattern sometimes that can be caught by static typing, like Signals

Sure - and you can test types in your unit tests using the OP's technique. :)