The only things that would necessarily need a whole new body would be anything of robotic nature, like transformers, etc. Otherwise, characters with alternate appearances need not be changed to human.

Characters like Sans, or MLP characters would be good candidates for Metamorphmagi and Animagi. MLP characters could have a human body they transform into and an animal form that they feel more comfortable in. Sans could appear in a skeletal form and have the ability to alter his appearance to a normal human form if he wanted to blend in better.