Again, you're making a lot of assertions in absence of any evidence to support them. One would think that this would be easily demonstrable seeing how long Haskell has been around, and yet no such evidence exists to my knowledge.
I think there is plenty of evidence (of how types help to design better APIs), you just don't want to accept it. I already mentioned LINQ and lens, another could be parser combinators and FRP (Observables in particular).
