I actually think a "System" QB applies moreso to college players than NFL. NFL QB's can adapt to other schemes and packages better than a typical system player. I would love to see an argument for Rodgers being system as he plays under center, shotgun, bootlegs, moves whatever else he does. I personally think a system QB statment does not apply as well in the NFL. Big league QB's typically have some ability to shift from different packages and play effectively. I guess an argument can be made for a QB that thrives in the West Coast but struggles in a pass heavy deep game.
I always looked to system QB's as players in college, so here are some examples of system guys:
Texas Tech runs a stereotypical system. Their QB's put up monster numbers, don't really translate to the league (Yes, I know Harrell...). Run out of a shotgun and pass the ball 90% of the time (at least in the 2000's). Timmy Chang of Hawaii was a system QB. If you want a great example of a system player from college who barely made it in the pros as a backup look up Kliff Kingsbury. College beast, nice arm, decent accuracy, always played in the shotgun and couldn't take a snap directly from the center when he got the the NFL, hence the system QB.
I fully expect to take some crap for this post.
I think you hit it on the head. System QBs are mostly in college. Players in the NFL can have a good game (Flynn) or a good season (Derek Anderson), but you cant make a career out of being a system QB. Defenses are too good and too smart for that.
And they dont win MVPs.