Sounds like you are trying to drag apps from the Start screen (Metro). We're talking about dragging windows on the Desktop to the extended screen. The TV is an extension of your Desktop, not Start screen.
That said, there might be a way to extend the Start screen, but it's beyond my knowledge or capabilities.
No, it is not that complicated.
When you add monitors (wirelessly-connected or not), you are adding the capability to have Windows either extend or duplicate your primary
display.
So, in my case, I have an SP2 running Windows 8.1; my primary display is obviously my SP2. When I project to the additional monitors (again, whether they be my DisplayPort-connected external monitors or my TV via the Wireless Display Adapter), I am either extending my SP2 screen or duplicating it.
By default, if I choose to extend, then the additional monitor(s) will show the Desktop screen; but from there, I can choose to show the Start screen and launch any Modern UI app on the additional monitor(s). Or, I can start a Desktop app. Or, I can start any type of app on my primary display and drag it to any of the extended displays. Whatever; the bottom line is that I do not have any restrictions; all I'm doing is adding monitors to which I am either duplicating my device's primary screen or simply extending its display field.
As Liam2349 indicated above, if you are going to extend your primary display, then obviously you need some sort of mechanism to navigate to and control content on the additional display(s)--but that's just a normal function of your device, be that via a mouse, pen, keyboard, touchscreen, touchpad, etc.