GTA would certainly not be an example I'd use for "great video game plot and characters" Tons of RPGs out there with great plots/characters, most Naughty Dog games, most Valve games, Bioshock games, Alan Wake, Red Dead Redemption, etc.
But Prince of Persia: The Sands of Time had a kickass story and characters, and they still managed to screw it all up for the movie. So even with the right game they can't seem to get it right. I still think it's because no good filmmaker wants to truly take them seriously as films, which is annoying. CBMs were a joke once too until filmmakers started realizing their potential.