I think NFL teams operate with this level of HC-GM power imbalance more than people realize. In the absolute best case scenario when a GM is the clear head of the HC, if the team finds any sort of success there will be a power struggle from the HC.
If it means anything, hopefully it means there aren't budget and "type" constraints on the process. The Bears want to idolize the positions of Head Coach so much (hence the aversion to mid-season firings), might as well make him the clear face of football ops and make it a big hire. Poles can run the personnel department.