I'd guess it's more like 5-10%.
There's probably another 5-10% that are problems dealing with trying to uniformly iterate over different kinds of structures, but I'm willing to admit I might just not know the correct way to do it (ie, map or fold or something).
There are plenty of languages like Haskell, Haxe, Idris, Agda, Roy, Rust, and Elm that get this right. Anecdotally it seems that most developers who advocate static typing aren't using these languages. It seems like the majority are writing in one of the Algol derived languages from the first paragraph.
Scala gets it half right with Option, but included null for Java compat. I've not written much Scala, but I've already encountered numerous bugs that resulted from some library returning an unexpected null, and the type system decided that was totally fine.
You can also add Swift to the list of languages that get it right in this regard. When receiving a return value from obj-c that can be null it comes back as an optional so you SHOULD safely transform it to a real value or only perform conditional actions on it. Of course there is the possibility to coerce it into the full type.