How is looking back and forth between your hands and tv intuitive?
How using an analog stick as a mouse or a D-pad to navigate menus more intuitive than a touch screen? (UI for OS, eShop)
Using the touch screen to build levels in Mario Maker is on another level entirely than using a regular controller.
Having a full map displayed on the Gamepad you can glance at while still moving is more intuitive than having to stop and pause. (Mass Effect 3, Darksiders 2, WWHD, Xenoblade CX)
Being able to access your inventory at any time on the touch screen is more intuitive than having to pause. (Darksiders 2, WWHD)
Looking at the gamepad to fine-tune a shot using the gyros is intuitive as hell. (WWHD)
Also, the updated touchscreen controls for Pikmin 3 are god tier.
Being able to map abilities to the edges of the touchscreen on each side of the map so that you have immediate access made Mass Effect 3 the only console version of a mass effect game to allow you to hot-key several abilities. It made that port comparable to the PC in that regard as you could mix tech/biotic combos on the fly without having to pause and bring up the power wheel.
How is it not more intuitive? Also, have you spent much time playing the Wii U? I only ask because your response mirrors those that came when the Wii U was first announced and no one had gotten to play with the controller yet.
There are games that came out in which the devs did a piss poor job on the port/use of dual screens, but that doesn't say anything about the controller and concept itself.