You are right about special challenges of managing Real Madrid which is much tougher than other clubs. Xabi Alonso past as player there would be huge plus. He already understand club culture how locker room works and intense pressure from fans and media. Instead of this he will not go blindly he know how to handle big personalities and high stakes building respectful team based on his shared experiences and knowledge of Madrid way.
Of course he knows how to deal with big personalities and high stakes because we are observing that he is currently engaged in the process of bringing about change in line with them. As far as I know, one of the interesting aspects of it is that there is no more space in the Santiago Bernabeu locker room, so many players are having to leave because Lucas Vazquez may not be with this club at this time. Perhaps soon we will see that Xabi Alonso's changing new chapter will come into effect because he has already taken on the special challenge of leading this team the Spanish team can consider some players as useless and send them out of the club as soon as possible.
At the moment it appears that Garcia and Mendy don't want to leave but truly one of them has to do it.