Probably you are mixing a few things up here. The View mechanism is limited to filtering lists of records. The capabilities are those you see when you press "Edit" or "Create New View" beside the picklist - that's it.
It is not possible, to integrate Reports in the List(views) picklist.
The option to override the View by a visualforce page is something entirely different and I would possibly call it a naming-clash. This "View" there means the view of a single record. You can open each record in salesforce either in "View" or "Edit-Mode" - both can be overridden by VF-Pages.
To get things clear in your mind think about the views in your screenshot as list-views and the overridable ones as record-views.
Another thing what you can do is to override the entire tab. And with that you might come a bit closer to what you want, since you could write there you own titlepage for your tab. As a tradeoff, you loose all the default mechanisms for listviews and you have to (re)create the picklist and all the logic you need on your own.