This has nothing to do with the ListView. It is the StackPanel’s “fault”. In a StackPanel the child items always consume only the space they need (in the direction of the orientation of the StackPanel). That’s how the StackPanel is designed. Use a DockPanel instead, there you can make the last item fill up all the space that is left over using LastChildFill="true"
(true
is default, so no need to explicity specify it).
<DockPanel Background="Green">
<Button DockPanel.Dock="Top">Text</Button>
<ListView DockPanel.Dock="Top">
<ListView.View>
<GridView>
<GridViewColumn/>
</GridView>
</ListView.View>
</ListView>
</DockPanel>