Alternate studios did not work for Call of Duty. It will not work for GameFREAK.
Besides there are alternate studios that provided Pokemon games in the past, the problem is the spinoffs all died out.
Pokemon Mystery Dungeon: Developed by Spike Chunsoft. Due to the 3DS entries bombing, there has not been any new PMD games since Super Mystery Dungeon. Spike Chunsoft has gone on to develop other games including games in their IPs.
Pokemon Ranger: Originally started as a joint development between HAL and Creatures, Inc. The games didn't do so well and HAL left to focus on Super Smash Bros. and Kirby full time. Creatures returned to focusing on the Pokemon main series only.
Pokemon Pinball: Originally started as a joint development between HAL and Jupiter, HAL would leave the series to focus on Smash and Kirby full time leaving Jupiter to handle the second game. While the series did well, Jupiter would find better success with Picross and they have been stuck developing Picross games ever since. There have been no new Pinball games since Ruby & Sapphire.
Pokemon Rumble: The series is handled by Ambrella. Every game has not done well, but yet somehow gets green lit for new sequels. Ambrella's latest game is Pokemon Rumble Rush for mobile devices.
Pokemon Stadium/Colosseum/XD/Battle Revolution: Originally Stadium 1 and 2 were handled by HAL and Nintendo EAD before moving over to Genius Sonority with Colosseum. The Genius Sonority games didn't go so well so the Stadium series was retired following Battle Revolution on Wii. The Stadium engine would be repurposed as the battle engine for the Pokemon 3DS main games. Since leaving the Stadium series, Genius Sonority would only handle a couple of Pokemon puzzle games since (in the Trozei series).
Any other games would be one shots at best. So basically any other developers either have moved on or found themselves stuck in a niche and can't expand.
EDIT - Ninja'd.