I don't think it's fair to say the Packers offense is nothing but Aaron Rodgers. He's of course the most important piece, but the O also features one of the best running backs in the game and one of the best offensive lines.
If you're using 2013 as your exhibit A, consider that (among other losses, like Cobb), we also lost our backup QB right after losing Rodgers and were down to our practice squad guy with Tolzien, who really had no business starting an NFL game that year. I can't say whether or not Wallace would have been successful, but by the time we brought Flynn back and he was starting, he kept us in every game but one and went 2-2 as a starter including a big comeback win in Dallas.
That 2-2 is much more indicative of what we should realistically expect from our backups, guys who can at least give us a chance with the talent around them. There's talent there besides Rodgers, but I think even the best teams in the NFL would struggle if they had to resort to 3rd string /practice squad /street QBs. Look what a disaster the Cardinals were by the time they limped into the playoffs last year.