Remove `utils.nextUpdate` method and `instance.componentDidMount` overloading

Clean up the tests a little since it seems these hacks are no longer necessary as React will render immediately when setState is called so any asserts can be make directly after this without needing to be async. All tests pass for React 0.11 and 0.10 but breaks at React 0.9 (which is when a lot of this code was written).

See https://github.com/facebook/react/pull/1293#issuecomment-50225018