Hang on...
The narrative is that De Rossi has been a nightmare to work with. Sacking him (after a pretty inauspicious start this season) isn't necessarily a mistake. You could argue that appointing him in the first place was a mistake or that giving him that contract in the summer was a mistake, but not sacking someone just because the Ultras love him would also be in itself a mistake.
The same would be true of giving Coleman another year. I think everyone appreciates that the lad is a great servant and at his best was one of the best full backs in the league, but there's hardly going to be uproar if a player of his age, who has struggled to keep fit for a while now, is told his services are no longer required at the end of the season. Giving him a new deal on the basis that the fans might appreciate it would be nuts.