De Rossi managed to make Roma a better team and not boring to watch. I agree with you that Mourinho is a great manager and no one doubts it. However, I think Mourinho's tactics are less effective at the moment. I don't know whether Mourinho is not adapting to modern football or Roma does not have players who suit the style of play that Mourinho wants to implement. But the point here is that Roma must give De Rossi lots of opportunities to build a solid squad and that takes quite a long time.
Every coach has his own tactics and style in training players on any team. And so far it has also been clear that De Rossi has been able to provide what the Roma players want so that the performance of the Roma team itself also started to be a little different when De Rossi handled it. Even though Mourinho is also an experienced coach, this does not mean that the way he trains can immediately suit the existing players at Roma, so the Roma team management has to take another option by bringing De Rossi into the Roma squad.