Wouldn't teams who are built to win now want someone who is a proven starter/veteran QB? I mean if you're built to win now you generally don't have the time it takes to develop a QB and the additional time to find out if he's the guy. The Bears already wasted 3 years of an elite defense waiting to see if Trubisky is the guy. It doesn't make a whole lot of sense to waste additional years on another young guy who needs time to develop and who may end up not even be an upgrade over what you had. A SB caliber defense has at most a 5 year window the clock is ticking.
I wouldn't be as concerned with Rosen's inexperience given the circumstances he's had to deal with in his two NFL seasons.
Chicago should be concerned about Mitchell Trubisky's high school level arm talent.