Of course a manager should resign if he knows he's not fit for the job. That's what a professional would do.
And I'm not saying Rodgers isn't professional. I just don't think he realizes he's not fit for the job.
Dude this a job for him. If you were being paid millions and knew that if you got fired the severence package would set you up for life would you resign and lose out on all that money. No, no one in their right mind would