I don't see your Wii argument holding up. The innovative thing of the wii is the controller. Nintendo would simply release their "Wii Controller" for console X which is required to play certain nintendo games for it.
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Corporate Trusts = bad
Different companies making different games, please.
Why have a controller that is only to be used for certain games? Kinda not so standardized.
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Wait, the Wii has different controllers for different games...
My point is, no one would take advantage of such innovation, and also, namely, that such innovation would never get built. The gaming industry would start becoming even more "same-old, same-old" than it already is.
DDR Dance Pad, Donkey Konga Bongos, headseat microphone for many games across platforms, n64 games came with ram expansion, gyromite for the NES had ROB, even as far back as the Atari VCS there were the paddle controls for certain games.
If everybody owned the same hardware, innovation could still be had through addons used by multiple games.
It's not just about hardware. Console's software tends to follow the original vision of the console it's running on.
A good parallel is Mac vs PC. What there is of Mac software always follows the slick and simple feel of the mac. Even homebrew and emulators on the mac are simpler and more friendly than their PC cousins. Most software is also centred around standards by apple and their collaborators.
PC's on the other hand are a jumble of different feeling applications fighting for their own standadization.
This is one thing on your home computer, but for consoles, "keeping things simple" is much more important.
The same thing would happen on a single cover-all console as we see on PC. In fact I think it would remove the goalposts completely. A peripheral and software standardisation fight would go on, with everyone having a different vision of what the customers want.
In the end I think it would also be at least as expensive.
The bongos, dancepads, eyetoys, r.o.b.ots give great variety as add-on peripherals, but historically, they've only really been used on one game (or one series of games). There is also a smaller budget for games released that need these add-ons as not many people own them.
Where as on a specific console, developers know that several million playstation3 owner will have a 6-axis dual stick controller and wants the best HD graphics... several million wii owner has a wiimote and wants good multiplay/party options... and several million XBOX owners want good graphics too and good internet gaming options.
I don't think all these different gaming "comunities" would happily live under the same roof, how could you possibly make one console that caters for everyone? If the wii is for people who want cheap fun games, and the PS3 is for people who want expensive HD graphics, how can one console deliver both needs? Cheap and expensive just don't live together.
...Also, how much would this "single" console cost? Without the cut that the developer gets from games, how much would they have to charge for a console alone to make it a worthwhile profit? For a start it would have to be powerfull and adaptable, that wouldn't be cheap. How much would the PS3 cost if sony wern't making an early loss on the console because of their long-term stratagy? A grand?
Only the console war losers would agree to this. the others will be making money and so won't give a toss.
No choice = big brother.
All I know is that I still scrounge for the LaserActive, and think it's one of the best conceived of pieces of hardware ever.