Why would pasting be even better (or useful)? Do you mean pasting direcly into the App Structure panel? I would probably prefer to paste in code view anyway - to be a little more confident that I knew exactly where it was going.
I would have thought pasting was the easy part; just a click and a keystroke. Copying, while not exactly difficult, is the fiddly part - clicking before the parent element, having identified the closing tag, and then shift-clicking or dragging to the end. A quick option for this - just by selecting the relevant app structure item - would be a very useful feature.
As you say, the right-click is taken, but I suggested adding a copy icon somewhere on the existing panel (to keep things simple).