Why doens’t the statistics include visitor counts, it’s usually more interesting to see how many unique visits you get, than page views as the same person could be viewing multiple pages giving an inaccurate portrait of site users.
Is this an option I’ve missed somewhere, or is this just not available at all?
The features you mentioned are not available with Jetpack, yet. Until then, you may want to consider using Piwik where everything you mentioned is available and much more! There are plugins to integrate Piwik with WordPress too, even though it works out of the box like a “Google Analytics”.
There are some disadvantages of using Piwik too. For example, it needs a separate database (technically only tables) to hold the visitors’ data that can grow tremendously, if we don’t keep an eye on the DB size.