Quotes / Barefoot Cartoon Animal

Films — Animated

Rich Moore: Okay, next question. "Did you ever consider giving Zootopians shoes, since they are clothed, or were they always barefoot?"
Byron Howard: They were always barefoot, because it looks weird.
Rich: Yeah.
Byron: Putting shoes on animals is weird — try it with your cat! Doesn't work!
Rich: Your dog HATES it.

—Zootopia directors Byron Howard and Rich Moore, justifying the film's use of this trope near the end of a 50-minute Q&A

Video Games

Ash: How do you get through all your crazy adventures without any shoes?
Sam: The same way you get through yours without a hat.
Ash: But I don't need a hat.
Sam: Exactly.
Ash: That's not really an answer.
Sam: Isn't it?
Ash: No. It's not.
Sam: And that's why I don't wear shoes.
Max: And also because shoes make him look like a big brown clown.

—Poker Night 2

Webcomics

I think you are close. Clothing is a prop. It highlights certain aspects of the character, but it also highlights the character's role or personality in a given scene/setting/sequence.
With animal characters, I'm guessing shoes play less of a part because animal paws are better adapted and more socially accepted bare. Furthermore, the paws help remind the viewer these are "animals".
But, I'll just have Vicki quote from Babs Bunny, "Don't I have the cutest toes?!"

—The World of Vicki Fox creator Michael Russell on why many cartoon animals go barefoot.

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