is simple and can be described in one or two sentences.
They are one-dimensional. They have only one aspect to their character which never changes. I always think of the Spice Girls--one word like posh, sporty or baby was intended to sum up the entirety of their character. That's as flat as you can get.
A character who doesn't change, it is the opposite of a dynamic character.
A Round Character
This is a simple or flat character, often used as a foil of the complex characters.
A flat character is uncomplicated and doesn't change during the course of the story. Vizzini is a flat character in the princess bride as his character doesn't change in story. *A car salesman who tries to bully people into buying a car.
Why not? It can be done. But the stereotype you refer to can also be the basis for a rich character of heroic proportions. Nothing says that such a person has to have a flat character. For example, such a character can have 'street smarts', or can have a passion for one cause or another that is not widely known, or an immense, courageous heart.
It's not a good idea to have a flat character be a major character. You want your major characters to be well-rounded and have actual personalities instead of just being stereotypes.
Flat
John procter
A Flat Character
the character is flat
Yes, but they usually aren't. It takes more effort to make a round character than a flat one, so most authors don't waste the time making a minor character into a round one.