There's a reason he hasn't been given that responsibility. Apart from the fact he lacks certain necessary qualities like awareness, control and composure under pressure, and mobility specially off the ball, he also is an incredibly inconsistent player. He is capable of giving you masterful performances, but also incredible duds.
CM for Barcelona needs to be a constant and consistent presence. Much of the team's play depends on the play of both the CM and the CDM. Cesc is not an ideal player to run the midfield for this team, IMHO.
The biggest reason is that no one has the balls to drop Xavi and Iniesta and Cesc will always be dropped for them.
He played alongside Xavi on the opening game of the season and assisted four goals and next game dropped.
The possession that the team had against Granada was the highest of the season.
Cesc is blamed far too much for the failure of him Iniesta and Xavi to play together. In the majority of games Xavi and Iniesta have been just as bad bad all the anger gets vented at Cesc.
This team doesnt need another Xavi, for one they wont find one and two the style Xavis game is based on has in a lot of ways been worked out by other teams.
I am not saying Cesc is the answer but what I am saying is that in my opinion he has not been given a fair shot to show a midfield of him and Iniesta can work.