I am not sure why you guys are hung up on the feature of playing the main console on the controller's screen. It is simply one of the features, and if it isn't one you would use, then so be it.
The examples of Nomad and Turbo Express aren't relevant. They are not second screens, and one of them came out long after the systems prime. Just because one of the features of the Wii-U controller is the ability to play the Wii-U games directly on its screen doesn't mean it is the sole purpose or even a primary one.
Who knows how well the second screen will be utilized, but this will indeed be the first time one was included with a console as a primary feature. Not counting the Dreamcast of course, because we are talking a completely different kind of screen here.
It's probably time for people to accept that there is a point in their day when they need to turn off the screen and go amuse themselves for a while. It's bad enough now that there are 3 screens available in every room to a kid (TV, PC, Phone, iPod, uPod, gayPod, PodPod, *Pod). Now they need a way to seamlessly transition a game in progress from the console to a standalone without even pausing the game? What is next? Holding the game in the controller like a burning ember and transferring it to a console in the other room? Holding it in the controller and riding in on a bike like the Olympic torch to a different kid's house?
This is starting to feel like freakin Jurassic Park. Everybody is so hot on what we can do that nobody is stopping to ask whether or not we should.
Huh? 
Agreed. And I don't think that people are getting that it isn't the ability to play the game on a dinky screen that's the feature, it's the seamless transition from big screen, to small screen, to a portable game you can play anywhere in the house that's the feature, NOT the fact that you are playing the game on a screen on the controller.
If I'm in the middle of a boss battle and I need to take a wicked dump, it might be nice to be able to bring the contoller with me instead of waiting 15-20 min until I'm done.

Also if a show somebody wants to watch is coming on and I'm 5 minutes from the save point, they can go ahead and watch their show, and I can watch it with them while finishing up.
Those kinds of situations are the feature.
Is that a feature that is going to sell me the console? NO. Does it seem like a really cool one? Hell yes!
I also agree about the lame, non-comparable examples people are giving. Stuff like the sega nomad is a portable version of the home console, that is NOT the same thing. And screens like those on the dreamcast, well those were so low res and tiny that it was laughable that any developer would be able to do anything really useful with it. So yeah this is the first controller to have this feature, and we'll have to wait to see what's done with it. I still have my doubts, but I'm not going as far as calling it a dumb idea.
And in regards to the comments about sony being able to do the same thing... well, sony COULD do the same thing, and they probably will claim to do it at some point, but it won't be as good. Why? Because Sony won't take the risk involved.
Nintendo, love em or hate em, has balls. When they come out with an innovative controller design they don't say "this will be an accessory" they make it the main controller that comes with the console!! That means that developers are pretty much forced to use it in some way and thus the unique features of the controller actually get used. This is what they did with the wiimote and while some third party implementation's are questionable we can all agree that most wii games make use of the wiimote. Compare that to the move. Sure there are some games that use it, some that use it quite well, but it's a small percentage of their game library simply because it's an accessory controller and not the main one. It does make a difference. The only two accessory controllers in the history of games that had a wide acceptance base was the genesis 6 button and the psx dual shock. The reason? The original controllers were broken and couldn't play the games of the time so developers and users were FORCED to use different ones.
Now while I'm positive that we will see a select few games on the ps3 offer streaming capabilites to the vita, it will be specific to each game, awkard to use and overall not be as seamless as the wii u's version. And if it isn't available for every single title then what is the point?