It's not, specifically, a technical issue nor a bug. It's a short-sighting in the design of the game's association. When a program starts up it logs and records the association of a device to the host [i.e. the computer] through the script currently active that the device uses to cooperate with Windows. The issue is, the game doesn't "refresh" this data because it does not have a direct association or access to the USB control drivers.

When you plug in a USB device it goes through a process known as Enumeration. This Enumeration tells the computer what kind of Device it is and assigns a unique Device identifier. The wireless controller is the actual 'Device' in this case, regardless that the receiver is still on [because that only translates the wireless signal to USB] the very act of having the controller on and associated is what keeps that value. Turn the controller off, the value is lost and the game is still stuck on the old one. When you plug it back in or turn it back on the game is no longer in a state of looking for peripherals. The same thing can happen in games when it comes to some Microphones/Headsets. I myself use a bluetooth headset for Voice Communication on MMOs such as Dungeons and Dragons online and DC-Universe. Turn off the headset and turn it back on, the game won't recognize it. I have this same issue with the PS3 and Xbox controllers with DCU as you all and I do with FFXIV.

If you think about it, FFXI works fine with controllers because it launched first on the Playstation 2 and already had the idea of game pads and their control function settled into it. By the time FFXIV is ready for the Playstation 3 the developers will have this issue sorted out by simply including an In-Game gamepad awareness design from the PS3 build. Easy-Peesy. Just comes down to developers remembering that we play with Gamepads, too, and to simply recognize the buttons of the controller isn't enough.
Of course it would be nice if I could find a way to force a device to have the same IRP every time it's connected. I'm sure there's a way, but usually there has to be a significant demand, first.

I would also like to see GamePad/Keyboard switching. Who hates trying to type and forgetting to hit that spacebar and suddenly your character starts to run in circles and all the names disappear over players?