Real Madrid will definitely prevent Mbappe's ego. Ancelotti is a great coach and resolving situations like this is his specialty. I'm sure he thought about these during Mbappe's transfer because Mbappe had great tolerances in PSG. Their privileges over other players were obvious. I know, like everyone else, that this will not happen in Real Madrid.
I also think that this kind of ego thing from Mbappe was already thought about by Real Madrid when they wanted to recruit him into the Real Madrid squad. And what you say is also true that Carlo Ancelotti can definitely handle things like that at Real Madrid and keep the atmosphere peaceful between all the players. Because Ancelotti not only has experience in training any player, but also has a way of not giving birth to any ego in any player he trains.
Carlos Ancelotti is one of the legendary coach in current era, and he understands how to handle things at this level with currently he is having too many star players in his team, and he is having experience of handling too many stars in years with we have no complaint from any player about him with he also never had any problem in past as well with this now Kylian Mbappé also understand now he is at the different place with different level so he will be also tried to change himself because Real Madrid is the biggest brand in soccer.
PSG was completely different place with they were having special treatment and many privileges for the star, but now we will have all changes from next season, and he could be jumped as normal player with having place into legendary club which is already having too many achievements into their history.