Feet are rarely given places of prominence. We don't dress them up in neon orange leopard print or put bells on them unless we are playing a jester, in which case they are dressed up precisely because they are considered a somewhat ignominous part of the body. Generally speaking, our shoe choice is calculated so as not to draw particular attention to our feet, a fact that belies their importance.
While they may not be the stars of the show, shoes are an important part of our costume. Footwear effects our balance and the way we walk, which is the physical foundation of a character. I usually rehearse barefoot, and even dance shoes slightly change my connection to the floor and my sensation of balance. Also, you just feel different in a pair of dress shoes than in sandals, and different in sneakers than in boots. That pair of crocs can help define your character's signature slouchy shuffle.
This is also why performing in your everyday shoes can be problematic. Your favorite Chuck Taylors feel just like you. They probably even look like you. It will make you feel normal and everyday, leading you to stand and walk in your normal, everyday way. Which is great if you're giving a power point presentation as your natural laid back self. If, on the other hand, you are trying to portray a stylized version of someone who is not you, it helps to rehearse – and then perform – a mile in their shoes.