Roma agains getting negative results and so far have not been able to win a single win in the 4 matches they have played this season, previously many hoped that de rossi would be able to get their first win when they managed after hold Juventus to a draw in the previous match, but what we saw in the match against Genoa was actually very disappointing considering the many chances created in that match, since the first half started Roma managed to dominate the match and even many chances that they were able to create, but unfortunately they wasted too many chances in the match, Dovbyk and Stephan El Shaarawy who have been Roma's mainstay since the beginning of the match have not been able to optimize the opportunities that exist throughout the match for more scoring, seeing what happened in the match against Genoa, The effectiveness of the game and also the finishing must be De Rossi main task to improve at this time if Roma really wants to win the next match.
Typical story. Ten Hag also showed more or less good results in his first season at United. But when you need to show results consistently, then class shows. Roma bosses sacked Mourinho and as I expected in the coming years they will only dream of achieving what was achieved under him. Roma is an ordinary mid-table club, to rise higher they need funding at the level of Napoli (and also for many years in a row) and not expect Mourinho to come and make magic (although he did).
Bringing De Rossi was not the solution to Roma's problems because the problem is still there. The players played very well in his arrival and he won some good number of matches before the real problem started again. If Roma wants to always finish as top four, they need to put the team in a quality standard by getting good players to strengthen their performance.
Your argument is valid. Mourinho has been a coach known to demand quality players to meet the target set. Without new qualified players' support, even for a coach like Mourinho, it would be challenging to take the team up more than one level. So, maybe sacking him without really providing for player recruitment is not the right move.
Rebekah replaced De Rossi and I think this does give an initial boost to Roma but, as you said, the fundamentals at Roma have not changed. What happens is maybe the players can play well for a couple of games. However, the problems remain similar: without raising the quality of the squad, they will continue to finish top-equalizers rather than actual top teams. To be able to compete at the very top and do so on a regular basis by finishing in the top four consistently, what Roma needs is to bring in players who can bring that stability and quality with them into every line.
We have seen this when he was coaching Chelsea, Real Madrid and Manchester United even with Roma themselves. Mourinho cannot win a title with weak players because he does not know how to start building an average player to become a superstar. He love professional players.
The club's management lives in a fantasy where it is possible to make no big investments but still get great results. 
