This bug has been around for a while but is still broken in 4.6.11.

Using an iPad, any OS version, you can't select a dark theme because the menu won't stay open to display the light and dark options.

 

 There is a workaround. You can hold down on the Theme option, the pop up context menu will open...

Then tap anywhere else to just cancel it, and the theme menu stays open, allowing you to select auto, light or dark...

 

I can confirm this from my iPad as well.