Compare results achieved by Mourinho and De Rossi, it's unfair to sack Mourinho and hired De Rossi then end the last season with worse result than with Mourinho in two season ago. In money spent for transfers, it's more unfair between Mourinho and De Rossi.
I really don't know what's happening in Roma recent months and why they decided to take risk and spend too much money for transfers like this. In the last months of past season, there was rumor that they considered to sell their captain player for finance improvement. Now, in this summer, things changed considerably and they did not sell players to get money but actually have net positive transfers with many big transfers.
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.