People keep saying the Wii U is weak... Too weak for what? FPS games? RPG's? I wonder what games could not be created... Sounds to me like wishful thinking. So far the weakest part of the console seems to be the DRM. I wonder if the added power of the other consoles will truly add anything or will developers be delivering the exact same types of games we have been playing since the PS2. I guess only time will tell but in retrospect did the PS3 deliver a single game that could not have been done on the PS2 but in SD?
It is an interesting question with many answers. Given that the Wii can emulate probably everything up through the N64 given a chance then yeah it could run pretty much any of the gameplay styles save perhaps mega RTS and simulations at that scale (though you just say something like cloud/server side and that vanishes if you want it too --
http://www.illyriad.co.uk/ might be a nice example).
If the Wii U hardware is hard to code for (and interesting float performance/techniques, bad SIMD and worse multicore would rather make it the case) then it means either building something from the ground up, radically altering your existing codebase compared to other platforms doing something else entirely. In high end software development, especially one where engine reuse is a thing, that is almost as killer as it simply being underpowered (start over and radical change are dirty words in just about every field that aims to get something done™). It would then take some serious incentive (and the very real possibility of bugger all sales is anything but) to go in for the Wii U.
PS3 and PS2... that is not a simple question. In many ways that would be a yes but in others the actual hardware/memory/general levels of resources skyrocketed somewhat. Also given the PS360 is still effectively running at SD a lot of the time.... (see all the upscaling stuff in later games). I am inclined to say no but I might see it happen for the PS4/xbone and current consoles on various levels.
People have been saying that the PS360 lacks the resources to create truly big levels for games. How much of that is truly a technical limit, a technical limit that could be worked around by streaming some stuff into memory properly, an actual game design decision, a game design decision made because of no money/open world is hard or something else is very much up for debate. I could probably generate examples for each and every one of those and they would hold up against a call of "but skyrim/just cause 2".
On technical workarounds. These require proper thought at the coder's level and maybe even before then. If the new consoles simply have more resources you can abuse then this could change things (optimisation is hard, time consuming and very very boring). History has born this out as well -- where devs were wringing every drop out of the old hardware the new stuff can and did allow for johnny just finished a java programming school to make things with nearly the same end result as one that knew the old hardware inside and out. As coding elegance and prowess matter surprisingly little in the face of actual results this becomes something worth noting. On the flip side my dev team might now include 5 types of texture artist where before a 3d modeller might have done, to this end some are already predicting budgets can not afford to balloon too much more if the same three/four markets are to be the main thing that is tapped in the same way as before (and nobody is looking to be doing anything too radical here). Of course giving said big team a bit of breathing room can make for a few good things and the actual results thing does come back into play here.
Spinning it once more the PS4/xbone could afford a lot of interesting techniques as far as AI, dynamic generation of content, possibly physics and more go and that could make the Wii U a running joke when it comes to ports. Personally I hope it is explored but I am not overly hopeful such a thing will happen any time soon.
In short you are unlikely to be troubled by any one style of gameplay, especially if constrained to a normal 20 hour game, but it could take quite a bit of effort to do and more if you plan to do it across several platforms without the Wii U being lead platform. As coder time and effort is a precious resource you do not need to be spunking it away if you have money to make so it could see the Wii U being snubbed.