I don't think that it's Rodrygo that is anxious of leaving Real Madrid, rather it is his manager that is pushing for that moves because he feels that Rodrygo isn't given enough time to play on the field. Left for Rodrygo alone, he still has passion playing for Real Madrid and believes he will definitely get on spot as part of Madrid first eleven in future.
You are actually right and I also share the same sentiment with you here, Rodrigo has always loved real Madrid just as valvades, he did not wish to leave the club, that's why he hasn't pushed for a transfer away from the club uptil now.
As for xabi Alonso's take on Rodrigo, it's very obvious that he doesn't rate him that much, so moving away from real Madrid is the best possible scenario for him and for his playing career, if not his value as a player will drop even more if he continues staying on the sidelines at real Madrid.