Yes, there are still many invalid states within a strong type and static typing is just one form of reducing complexity. I'm actually much more interested in cleanliness of design and architecture, but the String vs DateTime or Enum vs String examples are easy ways to illustrate the idea.
I had to implement a `Lowercase` type which is just a string that can only be lowercase (for case insensitive searches). After implementing standard traits like `Into` and `Deref`, it just acted as a standard string. That way I could guarantee at compile time that things are lowercase, but still have the flexibility of strings.
Another common idiom I have seen is to compose finite state machines using enums. You can only create a particular state from another state etc..
If the original simple argument were true, then everyone would introduce static typing, it would be a no-brainer.