After so many years it's still shocking how willfully people buy into third party excuses. Third party support isn't about horsepower, ease of programming or even sales. It's first and foremost driven by bias.
You really think hardware design decisions had nothing to do with this? It's the only thing that makes sense. It's a problem that began with the N64. The N64 had the specs, but cartridges hurt it. An N64 cartridge cost something like $10-15 to manufacture vs. only one or two bucks for a CD, yet could hold only a fraction of the data. The biggest N64 cartridges had a capacity of 64MB, while a CD can hold up to 700MB. Indeed, the average PS1 game was much larger than the largest N64 game; FFVII, the game that tipped the scales in Sony's favor, weighed in at over 1.3GB, so big it needed more than one CD. You try cramming that onto an N64 cartridge. The GC's format was less of an obstacle as the gap was reduced from a minimum 11 times difference to only a minimum 3 times difference, but that 3 times was still a probable obstacle, plus we have at least one dev on record saying that the GC having less main RAM than the PS2 and Xbox was an issue.
As for the Wii and Wii U, they have specs that make the one generation behind power-wise. The Wii wasn't much more powerful than the OXbox, and the Wii U isn't all that much more powerful than the 360 & PS3. That's a serious issue, hence why the Wii had few AAA third-party games and why the Wii U's third-party support was limited to some latter-day seventh-gen games and a few cross-gen games. CoD was the only major third-party AAA series that made it to the Wii (except MW2), and even though CoD was never a shining example of cutting-edge technology, even it experienced significant downgrades just to get those games to work on the Wii. But GTA 4 & 5? Oblivion & Skyrim? Battlefield 3? FFXIII? Far Cry 3? Red Dead Redemption? BioShock? Assassin's Creed? Batman: Arkham? Forget about it. Third parties were never going to bother putting their full support behind such underpowered hardware. They mostly saw it as a dumping ground for party games and shovelware. The Wii U is going through the same thing. It was the first eighth-gen console to market, so what little AAA third-party games it got was more of an instance of "Why not?" It was obvious from the get-go that third parties were going to drop most support for the Wii U once they started shifting away from the PS3 & 360 and focusing most of their efforts on the PS4 & XBO.
It's always been hardware. If it was bias then the third parties would have told Nintendo to piss off back in 1991 when they were free to develop for Sega. They didn't. The SNES had the full backing of the major third parties of the time. And Nintendo has always had at least a token degree of third-party support even after the SNES. Acclaim and Activision made games for the N64. The GC had a decent degree of third-party support, albeit far inferior to that received by the PS2 and even the Xbox. The Wii did get a handful of notable third-party titles that weren't party games or shovelware (Epic Mickey, Mad World, a few Sega games). The Wii U did get some seventh-gen games and a few cross-gen games. Third parties would put their full support behind Nintendo if the latter would just make a conventional, powerful console using a standard format for once, something they really haven't done since the SNES.
And as for your comment consoles vs. handhelds in regards to third-party games, well...