If he were to run out of bounds its a waste. If he were to throw the ball away its a waste. If he gets sacked trying to extend the play to get a higher percentage pass that's too greedy if anything. That's reasoning that he'll always be able to fire off a 50/50 ball and flying too close to the sun while trying to get something better.
I actually don't think any of these situations are what set Rodgers apart though. These situations would be memorable and I can't recall any. My guess is that he'll make a guy try for a circus catch on the sideline or rely on a WR's yards after the catch in situations where Manning, Brees, and Brady would throw a contested ball. Something like that.