The PlayStation 2 and PSP versions of the game lack a playable Coco for player 2, due to hardware limitations. Crash and Coco with multiple enemies on screen, each with their own individual animations and actions, would be too much for the PlayStation 2 and PSP to handle. Since Carbon Crash uses the same animations as Crash, he replaces Coco in these versions, and as a playable character, Coco was left out altogether.
On the other hand, Crash hacker Hacc has found something in the PlayStation 2 disc that is pretty interesting. There is one additional skin in the game that can only be accessed by hacking it. You've guessed it - it's Coco.
Playable Coco(contributed by Tanner (screenshots))
As you can see by the screenshots above, it's possible to make Crash look like Coco, but that's about it. Crash with a Coco skin will move and animate just like regular Crash does (right down to the spin attack), so using this skin only changes the way the character looks. This suggests Coco was initially meant to be nothing more than a skin, before they decided to make her a separate character with a voice, animations, and skins of her own. Coco seems a bit out-of-character using Crash's animations, and it's been confirmed by the developers in a past interview that this was one of the reasons she was removed from these versions.
Since this skin is incomplete, using it makes the character's head get set in an awkward position while riding a Titan. The game will also freeze if you try to face the Coco boss in this skin. Strangely enough, it is possible for two players to use the Coco skin without any issues.