The performance of the Roma team under Mourinho was not as good as expected. Moreover, Mourinho's relationship with the management was not good. This is why Roma management fired a coach like Mourinho. De Rossi is not experienced enough. But that's not to say Roma won't improve with De Rossi. Maybe the Roma team players will be able to adapt themselves well to De Rossi's match strategy. Every coach has his own unique strategy.
De Rossi might be able to stabilize the team. But the Roma team is not strong enough. Roma management should definitely take necessary measures to strengthen their squad. If the squad is not strong, it is not possible to get consistent good performances from the team.
Roma must thank Mourinho, he has been able to deliver a major title that has never happened before. The Special One was also able to increase the number of spectators at the Olimpico, thereby increasing club traffic again. I think Roma management was wrong to fire him. The transfer of coaching staff to De Rossi also did not improve the Giallorossi's performance, in fact there was only a setback compared to before. I am pessimistic about this team next season and it looks like it will be difficult to compete in the top five.
The same problem that Mourinho complained about buying new players is what will still happen in Roma, if not De Rossi will not be able to be in first five next season. There are matches that Mourinho experience will make him come up with a tactics to win his opponent, but I don't think that De Rossi has such experience.
Next season will be difficult for De Rossi if he does not improve his game pattern. I might be wrong with my thoughts towards him but next season is what will determine if he can manage the Roma or not.