You're absolutely right some QB's are a better fit for certain systems. Some fit better in the West Coast Offense ( ex. Brett Favre, John Elway, Joe Montana etc) and some fit better in The Air Coryell/Vertical Offense like the Chargers and '99 rams run or ran(Dan Marino, Phillip Rivers, Kurt Warner etc) and some like Brady and roethlisberger (I think the steelers use a similar system as the Pats but Steelers fans feel free to correct me) play in a hybridized system called the Erhardt-Perkins offensive system.
A good example of your point is Brett Favre and Kurt Warner for example, Brett played in the WCO in GB, when he got traded to the Jets who ran a Variation of the Coryell Offense, he wasn't as good, not because he couldn't push the ball down the field vertically like the coryell asks, but the terminology was different then the WCO (The offense uses a specific naming system, with the routes for wide receivers and tight ends receiving three digit numbers, and routes for backs having unique names. For example, a pass play in 3 digit form might be "Split Right 787 check swing, check V") which can be very complex for someone that's a gunslinger like brett, and likes to move out of the pocket, which the coryell typically is for "pocket passers". Also you're supposed to throw to a certain spot on the field before the receiver gets there, it's based on timing and rhythm whereas Brett was used to throwing what he sees, or at the receiver.
Now Kurt Warner was the opposite, coming from the Air Coryell System that Mike Martz and Dick Vermil employed. The passing game was based on timing and rhythm, and coaching the system required a lot of repetition. It often puts receivers in motion. With the new defensive rules limiting contact to near the line of scrimmage, receivers in motion would be virtually impossible to jam. Coryell not only placed wide receivers in motion, he did so with tight ends and running backs as well. Putting the players in motion also had the advantage of allowing the quarterback to determine pre-snap if the defense would be playing zone or man-to-man defense, which Martz does a lot of. After getting beat to a pulp in the Martz version of the coryell system, when he went to the Giants he sucked because it wasn't the same system, when he went to Arizona and Wisenhunt took over it was a hybrid system that employed a lot of the coryell language and "system".
As a Bears fan I feel the Cutler would be a better fit in the WCO, with the roll outs, audibles, and quick strikes, thats why I think it works so well for Aaron Rodgers because he's a mobile QB, that's allowed to audible and hit quick strikes, whereas Phillip Rivers is
perfect for the Air Coryell, because he is a pocket passer who fits in Norv's "system"
Overall, you're correct in your point, but If I'm wrong about the systems please feel free to correct me.