...no, GamePad was failed from the get go. I thought about it much, and the answer seems to be that.
There are basically two ways to use GamePad: the sane way and the insane way. The sane way contains actually quite a few options besides regular sticks and buttons: off-screen play, local multiscreen, touch screen level editors, HUD transfer...
The problem with the sane way is that it doesn't sell the Wii U. At all. Off-TV, HUD and local multiplayer functionalities could be New 3DS bonuses, like Vita got it on PS4. Editors could be implemented with a Wii Remote, or maybe "Wii U Mouse" which could be way cheaper. As for actually innovative mechanics, GamePad is, perhaps, useful for boosting the creativity of game designers, but the end results aren't usually something you really couldn't implement without it.
Then, there's the multiplayer with people not seeing all the stuff. The problem is that while it may be obvious to Nintendo, a general gamer doesn't see why would it be advantageous over online multiplayer (the answer is fun with real friends, but also lag limiting game design). Even then, it's interesting they didn't show it off at all during Wii U reveal, while it's basically the basis of the most interesting Nintendo Land games.
Intermission - let's get to what OP is proposing. Except for adding more power into Wii U, OP's saying that the GamePad should have been its very own portable system. This IS basically 3DS. There are differences, like the thing not being packed in, but seriously. Unless we packed the whole Wii U into the thing, but even then marketing both that and 3DS at once (with separated ecosystems) would be absolutely crazy.
Anyway, as mentioned earlier. I'm of the opinion that most Wii U software is simply impossible to bind to the GamePad, unless you go the insane way. What's the insane way? It's taking gamers out of their comfort zone. It's "absurdal" use of GamePad that makes people embarassed. It would involve rapidly switching from touch screen controls to regular ones and back, or spinning around with motion controls instead of making subtle movements while using the screen since the TV doesn't spin with you. This is not only embarassing (for some), this is also tiring and simply unappealing.
I'm not exactly sure why Nintendo went with the GamePad after all.
The fact that Mario division boss didn't know about the second screen before reveal could imply something though.