I agree and of course they should be granted some time as new coaches when they come to the team and their main task is to do some changes to improve the team. But in the soccer business it is always the same. The reason why they fired Mourinho and now got De Rossi is because they want results fast. Otherwise they could have waited to change the coaches until the end of the season. I think this is the message they wanted to convey to De Rossi. They give him the chance now because they want results now.
It's very true that these new coaches needs some time as they are New to their team and will need the time to settle and get to know the team well enough to be able to know which tactical approach will best fit the team and that which works best for their team but coming in at the beginning of the season is usually challenging because the expectations are high already.
Mid season come with high expectations form coaches because boys usually expected of them to make up for the mistakes of previous coaches and see what they can do about the situation and making sure to fix the team and getting the desired results the fans and the management of the team requires of them. It's very challenging for most of these Coaches and they may have little to almost no time to fix all these before the end of the season.and this is the exact challenge Rossi is facing trying to make up for Mourinho's mistakes.