> Like, if you do type the arguments of a function, the optimising compiler will have less work to do.

Giving types for function arguments doesn't actually have any effect on performance: the compiler specializes on concrete runtime argument types anyway, so completely untyped code is just as fast as fully type annotated code—since the types are known when the code is compiled. On the other hand, giving type information is essential for performance involving memory locations, i.e. field types and the element types of collections.