I think it will be better if PSG lets him go to Real Madrid. What for to defend him? He has no interest anymore to play in PSG. When a player already has no interest to stay, it will be a worse decision to keep him in the club. Imagine if the player won't show his best performance in the next season? It can a big problem both for the player and the club as well. The player price may decrease quite a lot and probably Real Madrid will be no longer interested t sign him. I hope PSG management won't consider experiencing this potentially bad situation.
You have a good point, but it's not really that easy to let one of your best players go, sometimes players don't really want to leave, but they make it look like they want to, so the club can address some issues they prolly aren't comfortable with (most times it's wages). Then again it does not matter if a player wanted to leave a club or not, I believe as professional footballers they always play to the best of their ability, cause they are not just playing for the club, but for their individual accolades and development, thus even if PSG stop Mbappe from leaving, he'll still deliver his best for them next season.
Having said that, the real fear for PSG should be the rather short time he has left on his current contract, if they do not sell him now, they run the risk of him leaving the club for free if they fail to convince him to renew his contract as the season progresses; and for a player like Mbappe that'll bring the club millions of pounds if they sell him, it'll be a big loss if he goes for absolutely nothing.