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For Pikachu, it was likely to make it silhouette stand out more.
Compare old Pikachu to similarly-shaped Pokemon like Clefairy.
Ponyta is, well, a horse on fire, while Keldeo is meant to be cute in comparison to the other Musketeers to show that it's the youngest and most inexperienced of the four.
Vulpix and Zorua focus on different aspects of the kitsune. Vulpix is the multi-tailed aspect, while Zorua is the illusion/shapeshifting aspect.
Fletchinder is pretty much just a cartoony version of the real life bird it's based on.