This would be cumbersome since you have to drag your mouse all the way across the screen, pick up the object, and then drag it all the way back to your cursor. It would also be counter-intuitive because dragging an object implies you’re moving it – not copying a reference.
What about adding an option to the context menu? Granted, that too has its flaws. It would not be very useful on the client as it doesn’t support WaitForChild.