Not exactly what I was thinking of, it's pretty much a kid's movie, regardless of whatever message it tries to convey.
And if you've watched Cars or other Pixar movies, then you'll know that despite the childish appearance they're actually extremely well written, well characterised movies. Look past the childish veneer and it's exactly what you asked for.
Don't make the mistake of overlooking it just because it's targeted at a younger audience. Disney and Pixar put way more work into making sure that their movies are well plotted and characterised than most studios.
Now that I think about it, Cars has some things in common with a Western, with all the "stranger that arrives into town and helps us" kind of thing. Perhaps a racing movie that follows a Western-styled plot, like Cars, could be a good thing.
Watch the movie. That's not what happens at all.
Lightning helps the town a little, but the heart of the story is about Lightning's growth as a person. He's already an incredible racer, but he lacks the friendliness and honour to build a successful team around himself and the humbleness to ask for help when he needs it. He's never had a real friend, just lackeys and suck-ups.
In Radiator Springs, he meets people who like him for himself, not for his achievements. He learns what it's like to be disciplined, and develops a moral sense. He learns the value of hard work and loyalty, and listening to those who have more experience. He comes out the other side more mature, more skilled, and with a group of people who love and support him for reasons other than his skill as a driver.
It's a bildungsroman, a story in which Lightning grows from a hot-headed youth into a man. While some Westerns also share this basic structure, it's not exclusive. Westerns are defined by the time period and region that they're set in, not the story structure.