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Upgrading to a 1440x720 (720p) screen would require multiplying the Wii U's current dimensions by a non-whole number. As a result, the image quality would be reduced on one of the two GamePad types. If Nintendo (or other devs) optimize games for the current 480p GamePad, it would be like playing a GameCube on an HDTV. If Nintendo (or other devs) do the opposite, it would look like playing a PS3 on an SDTV.
Changing the resolution to 1708x960 (960p) would solve this issue...but that screen size isn't standard, so they'd have to be custom-made (thus increasing costs).
3DS: 4897-5935-1924; NNID: CrimsonEnigma; Steam: CrimsonEnigma ''If you think a system will make you look mature, you ain't mature'' -squatch22
Vita screen is 960x544 at 5", which works out as 220ppi. Wii U gamepad screen is 854x480 at 6", which works out as 158ppi.
My telly is 1920x1080 (the only device in this post that's considered 'HD') at 42", which works out as 52.45ppi.
Obviously the telly has the highest resolution by a long way, but it also has the lowest pixel density due to its size, and it's this measurement which ties screen resolution to real world measurements.
Calling something 'HD' doesn't mean it's better than other devices, it just means it complies to a standard.
As for a potential Wii U HD gamepad; I wouldn't buy one, as the increased resolution would impact game performance and introduce incompatibilities with games released before the new pad.
One of the potential problems for a hypothetical HD GamePad is bandwidth. We know that the Wii U can (or, "will eventually") stream to two GamePads, but we know that to do so, it reduces the framerate of the stream to 30FPS for each GamePad. This means that Nintendo are using more than half of the amount of bandwidth that they have determined will be readily available during normal use of the GamePad (since if they were using less than half, they could stream to two GamePads at 60FPS with no worries).
The problem is that the lowest HD resolution - 720p - has 2.24 times as many pixels as the GamePad currently does. Sending 720p to a HD GamePad would take approximately 2.24 times more bandwidth than sending the current 480p signal to the current GamePad, if the same level of quality were maintained. (It'd actually probably be slightly less as encoding gets more efficient if it has more data to work with, but it probably wouldn't be enough of a drop to push it within the bandwidth limitations).
This would leave two possibilities for 720p - either drop the quality, or drop the framerate. Dropping the quality is probably a bad option - badly encoded 720p video can very easily look worse than well-encoded 480p video. Dropping the framerate (to 30FPS) immediately reduces the bandwidth needed to something almost identical to the same bandwidth that the GamePad already requires, so that's very much a viable option. It wouldn't be great for 60FPS games but many games are 30FPS anyway - they'd lose nothing in terms of framerate, so they'd only benefit from the increased resolution.
However....there's one other thing to consider. Dropping the framerate to 30FPS would allow for 720p video compressed to the same extent as the 480p video is compressed now....but would also allow for 480p video compressed a lot less than it is currently, and that could end up looking as good as 720p would, cancelling much of the benefit of going to 720p in the first place.