No, that's a function of bad GMing, or bad breaks. Eli started because of both (bad GMing to put him behind an injury magnet, bad breaks that Warner didn't revert to his glory days like they hoped), Roethlisburger started entirely because Maddox got hurt. Smart teams season their QBs when they can, whether or not they can is often a result of injuries or out right player crisis (injuries, guys not wanting to train their replacement).
The New York Giants of the mid-1980s were a classic example of this . . . Jeff Rutledge was the backup to Phil Simms, while Jeff Hostetler was drafted in the hopes that he would be the future of the franchise -- and spent most of his first few years as the #3 quarterback.
The salary cap doesn't allow teams to have that kind of depth anymore . . . so the rookie becomes the #2 quarterback, and the #3 quarterback is some guy like Vince Evans or Jeff George who has been in the league for about 70 years and sits by his phone waiting for a call from a desperate team.