3rd parties want to sell enough games to make a profit to guarantee that they can stay in business to continue developing/publishing games.
They don't care what platform the game is being developed for and will work within the limitations of a platform if the yields are calculated to be worth the effort. For the PS3, development costs were higher and the hardware unconventional, requiring a different approach to coding. The 360 is arguably the easiest platform to develop for (particularly for PC developers), but even it has the issue of no standard HDD (which means all games must be made to run without this benefit).
Part of the problem with the Wii is the hardware itself. Not just the decision to use undespecced hardware, but the very motion controls that made the platform such a hit among those looking for something different or new. The Remote itself is awkward as a standard controller yet games that require players to use a classic or GC controller seem a bit out of place on the Wii. "Why no motion controls? Isn't that the point of the Wii?" The result? A lot of games that would have been better off with standard controls end up with tacked on motion controls.
This is not to say that developers couldn't get creative with the control scheme (as many did) it just really isn't suitable for most traditional control based games. You can't rewrite any genre with motion controls for the Wii and expect it to feel natural and be "golden."
The specs of Nintendo's next console won't be in question, making the problem of doing cross platform ports a non-issue from a processing standpoint. The only potential problem is Nintendo's next console isn't likely to use conventional controls either. So either all platforms have motion controls that can be ported with relative ease from one platform to another, or 3rd party developers are again left with the choice of doing sub-optimal ports, or lead developing games on a Nintendo console that can't be properly ported to other platforms. That would mean having to make their games Nintendo console exclusives (due to the lack of portability) which is would make them higher risk. Add to that the reality that dictates games on an HD Nintendo system with similar specs to any other platform will be just as expensive to develop.
Take the 3DS in contrast. Very capable hardware specs making processing power a relative non-issue for most projects, but conventional controls, meaning games could be ported to other platforms with the loss of the 3D effects, assuming that future competition won't also have portable 3D capabilities. Plus the 3DS should be relatively inexpensive to develop for (compared to consoles) due to the nature of portable games with their shorter development times and reduced resources.
