While I agree that De Rossi started awesome, but he did not finish well. If you check his first 10 games at Roma, you will think that De Rossi was a much better manager at Roma than what Mourinho did, it looked like they were going great and then they started to be even worse, so the return became not that great.
This of course is not something that we should be all expecting De Rossi to do bad or good this season, just wait and see. Mourinho was fine, but Roma basically said if they are going to pay that much for a manager, that manager might as well take them to UCL or at least somewhere decent, and Roma did terribly at the league with Mourinho, yes they won conference and finalist at Europa, but both years sucked at league, which meant not so good for them.
Among other things they didn't manage to keep Romero Lukaku, now Roma had to fall back on another striker, unfortunately he lacks let's say a little bit of being political. He certainly has great possibilities, sending Mourinho away like that wasn't nice after the things he had done. Mourinho had rejected the Saudi league for Roma.
After leaving Roma, he didn't go to the Saudi league, but Mourinho. If he really wanted to, he would probably be managing a team in the Saudi league now. I don't think he wants to leave Europe. I don't think money is a priority for him. Also, they didn't sign Lukaku, but Dovbyk came and I think he is a striker who can do good things. His presence is more important for Roma than Lukaku.