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).

Recently there was an article about a whole application: http://abailly.github.io/posts/cm-arch-design.html

I can also recommend book Functional Programming in Scala, which talks about how FP helps develop good API in more detail.