Letting Cutler go would create two huge question marks over the offense. First, we have no idea who would replace him. There's no guarantee a suitable replacement can be obtained in the draft, and there will certainly be none on the free market. The second would be Brandon Marshall. If Cutler goes, what happens with him? He's been very clear that Cutler is his quarterback. Will he become toxic and try to force his way out of Chicago? While I'd like to think he would be on his best behavior, the guy's past really says otherwise.
Then there's the defense. Emery and Trestman need to focus on rebuilding the unit. To do this they'll need some free agents, but most importantly they'll need to use the team's high draft picks. The first three or even four rounds should be defense oriented, with them taking the best DT, DE, LB or CB available.
Unless they can tag and trade Cutler for a king's ransom, he needs to stay.