At Real Madrid, it's not enough to play good soccer. It's also about satisfying egos, handling the press and winning trophies. This pressure is much greater than what Alonso experienced at Leverkusen. Alonso has a lot of potential to succeed in star management because he knows this environment as a footballer and he is intelligent. Xabi Alonso is also a former Real Madrid player. He knows the culture of the club and the dynamics in the dressing room. This could help him build a natural relationship of respect with the players.
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.