Does Sphinx (or any other automated-documentation tool) read the MyPy annotations, or would I have to type them in twice, in different syntaxes, if I wanted types in my docs + linting?

Or does type documentation not matter that much, once it's being enforced by a tool?

there is at least this, others might also exist https://pypi.python.org/pypi/sphinx-autodoc-annotation

Why not put type annotations in docstrings?

There's some discussion of this in PEP-484: https://www.python.org/dev/peps/pep-0484/#other-backwards-co....

Does mypy see any performance improvements over vanilla python (because types are static)?

No, the interpreters make no use of annotations.