Static typing gives you useful things (with a trade off), not having to write tests isn't one of them.

I disagree; static typing is, effectively, having an automatic set of tests automatically run for (by the compiler) you that you don't have to run/create/maintain yourself. As someone who's moved from statically-typed languages to Python (2.x), I can't count how many times I've made errors that "should/could have been caught for me by the compiler", if there were such a thing in Python. It slows me down in nontrivial ways. It would be good if we could use 3.x-series annotations to achieve much of the same thing, but the world hasn't gone 3.x yet.

Your point about the value of unit testing in general is well-taken, however.