Since he is young is the main reason, he should not be patient on the bench because he wants to stay in Real Madrid. Playing in Brazil national team has nothing to do with which club that he should play for. Only Rodrygo can decide what he wants for himself currently. Real Madrid is always recruiting players every season, and I think that they might not need Rodrygo if he doesn't improve his performance in order to win a place in Xabi first eleven.
What changed from him while playing for Ancelotti and when Xabi Alonso took over the position of the manager? I don’t think anything has as far as I know. His pattern doesn’t fit well with using Rodrygo and that is the main reason he needs to drop him off. Also, Perez has given him go ahead to drop any player he wishes to if they don’t perform as needed, so what he’s doing is for the interest of the club moving forward and also him retaining his position as the head coach of the team.
Rodrygo might be young still, but keeping him at the bench and wanting to wait patiently could distort his career from now, so he needs to get more playing time to prove himself more than he has in the past. I won’t advise that he stays back and be bench, let him try his luck elsewhere as more teams will be keen on signing him now.