And it was not obvious to me that the various list views I select from the drop down menu on my "Members" page should in this case be declared as Menu Items in their own right.
It seemed to be more natural that the views selected in the drop down selection box on the Members Page should inherit the template from the menu item they were placed on.
But, as you say, declaring each view as a separate menu item allows to set the template for each (although those menu items are not actually needed to call up the views from inside the Members Page.)
You may consider this as a wish for clarification/simplification.