I totally agree with what you say because sacking a coach like Mourinho is a big mistake, indeed at that time Roma was in an unstable condition but Mourinho was still able to bring his squad to compete in Serie A and also the European league, the conflict that occurred between Mourinho and also the club owner was the main reason for his dismissal, with the current condition of the squad, of course Roma needs the right strategy and also the right coach to restore their performance to be better, so indeed the investment they made in the transfer market last summer can provide a significant improvement, Ranieri has taken over the team now, with his experience and also his ability to coach, of course fans expect a lot of changes that will occur later.
Mourinho's 3 seasons in Serie-A as AS Roma coach, it can be said that AS Roma's performance is stable under Mourinho's direction, but only stable and does not show any improvement. Well, maybe AS Roma feels that they have given Mourinho enough opportunities and prefer to replace him. Actually there was an improvement when De Rossi was appointed to replace Mourinho, but it is quite unfortunate that in the new season De Rossi declined.
Either AS Roma is not very patient or what, because they made a decision at the beginning of the season when usually a team has not found their best form. Now AS Roma must start again from 0 with their new coach.