A club that won titles in several competitions such as Paris Saint-Germain, must have a very strong cooperation between players.
When a club has a selfish player, it is impossible for the club to get the title because of the chances of victory in each match greater if done together without relying on just 1 player.
So I agree with your opinion that Kylian Mbappe still has a selfish nature, it is impossible for Real Madrid to win the Champions League this season.
The problem is not just about Kylian Mbappe, but the number of superstars in one club. If I were a football coach, I would limit the number of superstars in the attack. Vinicius Junior, Rodrygo and the French striker all have ambitions to win the Ballon d'Or someday and this is making them selfish. Personal ambition could make players selfish. Mbappe is well known to be self-centered, he wants to always be the most important player on a team. His departure from PSG brought some level of cooperation in the club.
But I don't agree that Real Madrid will not win the Champions League because of Mbappe's character. It is the responsibility of the coach to change the mentality of these selfish players and make them know that they can achieve more collectively. The success of the club will give them more chances of winning personal awards. Carlo Ancelotti was able to achieve it, so Xabi Alonso can also achieve more with these top players.