The absolute, number one, ONLY reason I would not want a guy with supposed "character" issues, is if we're talking about a guy who supposedly doesn't care. Somebody who just doesn't like playing basketball that much.
My understanding of Cousins is that he's a hot-head who sometimes lets his emotions get the better of him on the basketball court or when he's dealing with his coach. If anything, it sounds like he cares too much at times. He just needs to learn how to handle and channel his emotions properly. Fine.
Give me talent. You can teach character. You can teach people to handle their emotions, to act more professionally. You can't teach talent (or size).