I firmly believe that Nintendo handheld consoles are just expensive Pokemon-training devices. Any other game in the Nintendo library is just fluff.
WHAT?! I'd say that most of the handhelds had a nice library of games that wasn't just Pokemon:
Gameboy: Pokemon Gen I & II (& Pinball & Puzzle League), Tetris, Legend of Zelda (Link's Awakening, Oracle of Seasons/Ages), Super Mario Land games, Metroid: Return of Samus, Kirby's Dream Land, Shantae, Wario Land,
& Others
Gameboy Advance: Pokemon Gen III (& Pinball RS & Mystery Dungeon), LoZ: Minish Cap, Metroid Fusion & Zero Mission, Mario Kart Super Circuit, Golden Sun, Final Fantasy Tactics, Mario & Luigi Superstar Saga, Wario Land 4, Advance Wars, Sonic Advance, Megaman Battle Network, Kingdom Hearts: Chain of Memories,
& Others
Nintendo DS: Pokemon Gen IV & V (& Mystery Dungeon & Ranger & Conquest), New Super Mario Bros., Mario & Luigi Partners In Time, LoZ: Phantom Hourglass & Spirit Tracks, Nintendogs, Kingdom Hearts 358/2 Days & RE:Coded, Spectrobes, Okamiden, Kirby Super Star Ultra & Canvas Curse, Rhythm Heaven, Brain Age, Scribblenauts, 999, Animal Crossing: Wild World, Phoenix Wright: Ace Attorney, The World Ends With You, Elite Beat Agents, Professor Layton, Mario & Luigi Bowser's Inside Story, Mario Kart DS, Mario Party DS, Mario Hoops 3-on-3, Tetris DS,
& Others
Nintendo 3DS: Pokemon Gen VI, Mario 3D Land, LoZ: Link Between Worlds, Luigi Mansion Dark Moon, Bravely Default, Super Smash Bros for 3DS, Kid Icarus Uprising, Pushmo, Zero Escape,
& Others
And these are just a few quick examples I pulled. I tried not to include ports and I missed many sequels that were on other handhelds. I'm also missing a lot of franchises. Honestly I have no set rule to my list, though if you check google for "Best Gameboy/GBA/DS/3DS games" they'll pick up the slack.
HOWEVER! I will agree that the 2DS was released specifically to help increase the sells of Pokemon X & Y. It was released on the same day & some special ones even had Pokemon X & Y downloaded on them (and I think even designed after Xerneas and Yveltal).