I don't think it is about handling egos, it is more about the fact that he needs immediate results.
iirc, it gas been very long time since a coach stayed after a season with no trophies. Perez beliefs if you don't win anything you leave for someone who can do it.
Alonso first season in both Sociedad B and Leverkusen was barely a success, but he was building foundations for great second season.
Madrid ain't giving him a year like that, and he needs to win some how, some way until players buys in his ideas fully.
There is no place for Arteta's type of bs in Madrid, you want to stay you need to deliver immediately. In that way Alonso was a bit of odd/risky hiring.