Real Madrid is a big team, so it's natural to expect a coach who can deliver success quickly, but it won't be easy for Xabi Alonso.
They are a big club but I am unsure that their team are big one and perhaps there are other clubs with more players in their team than Real Madrid. As one of most successful clubs in Spain and Europe, it's logically that their fans always expect their club to win titles in each season and Xabi Alonso will carry this burdensome task in his first season for Real Madrid.
In my observation, the uniqueness lies in Perez mindset, he has fired several great managers and some of them after winning trophies in the previous season. Perez ambition to win trophies every season to increase the club's income has made several great coaches fall victim, including Zidane, who has won the UCL trophy three times in a row.
Firing coaches has become a tradition at Real Madrid, and it will continue if the new manager fails to win a major trophy, including Alonso. This situation is very different from other big clubs, which consistently give coaches more than one season. Despite the fact that Ancelotti failed to deliver a trophy to Real Madrid in his final season, I don't think there was a compelling reason behind his dismissal.
There are other clubs that have habit of firing their head coaches very often, such as Chelsea, Napoli or PSG but Real Madrid manage to win many big titles from La Liga to Champions League. So this habit does not harm their club success so far and with Perez as their club President, they will continue like this with Xabi Alonso and any next head coaches until there is a change at President position of Perez. The man is old enough and surely his time as Real Madrid's President will not be too longer time.