I think blueobsidian's response hit the nail on the head. Just because we become better people for having lived through certain things, doesn't necessarily mean that we become perfect.
For example. When my grandmother died, I realized how much I had taken her for granted, how impatient I'd often been with her.
It took me a while, as a kid, to add up all the dots, but I started making a physical effort to be more understanding toward my remaining grandmother's, shall we say, grandmotherly instincts of constantly trying to feed me something, drag me with her to this place or that, etc. I haven't always succeeded, and certainly I'm flawed in lots of other ways, but I think I have become a better person as a result.
If a literary example is what you want, I'd bring up, perhaps, Nick Carraway from The Great Gatsby. He wasn't perfect before the story, and he wasn't perfect after, but I think he was changed. Gene Forrester in A Seperate Peace, and Ester in The Bell Jar are other examples. Or, recall Obi Wan Kenobi, Anakin Skywalker, and Luke Skywalker from Star Wars. All those characters undergo radical growth throughout the Star Wars Saga, but at no time are they ever "perfect."
On the other hand, I'd like to distinguish between character development and character growth. Character development is a necessity. It's basically getting the reader's acquainted with your characters. Character growth, doesn't always have to be, however. Take the nameless narrator in Dosteovsky's The Underground. I don't think there was any real evolution or growth during the book. Development, yes. Growth, no, not in my opinion. If done well though, it can make for very compelling reading nevertheless.