I under stand what your asking to a degree. Its not possible to control consoles through a computer, while performing normal computer funcations. Such as click a icon and play xbox, then minimize it, and start up internet explorer. Because thats utilizing completely different hardware togather. You can throw everything in a case, then play each one independently. But as you say a super console, all of them combined togather. Thats just not possible, since all that hardware is not compatible.
You can however connect consoles to a computer. Then have those image's displayed on your monitor. When you connect a console to your computer, your running everything from the console. I know their is software that enables you to play PS1 games, on your computer. So your using 100% computer hardware. The software reads the game, and your computer plays it. But people take this the wrong way. Graphics pretty much do not increase. My friend had that program, he was playing all of his PS1 games on his computer. No graphical increase, so a good system you simply would not benefit from.
Is their a software for gamecub, PS2, and Xbox. No clue. It would probably be pretty technical though. Im sure its not IMPOSSIBLE. But even for computer geeks, it is. That would take a large amount of programing.