I'm highly skeptical about the idea of Apple purchasing Nintendo and how well it would go.
Nintendo is a unique player in the console hardware market. Their top exclusives can appeal to younger audiences. Many of the best-sellers on PS4 and Xbox One that hear about are typically M-rated games. The 3DS is the most successful current-generation handheld. If Apple bought Nintendo and relegated all new Nintendo games to iOS and OS X, the handheld gaming industry could take a hit if 3DS production and game development cease.
If Apple decides to relegate the games to iOS and OS X, making a good touch interface for the new titles of Nintendo IP's is another factor. Developers that made great games exclusively for Nintendo IP's would have to figure out how they're going to get it right. There could also be a first-party controller and tvOS support for the games.
Provided that the games are executed correctly and iOS-exclusive, Apple could drive the mobile gaming market into its favor over Android.
However, there are also indie game developers out there that could have made games that are similar to Nintendo's games. Could they be killed off because, "Why would I buy this indie-developed Nintendo clone when I could buy actual Nintendo games on my iDevice?".
How would a profit that is sufficient to cover all development costs of the games be made off the IP's on mobile? I don't think it makes sense to sell a game for $20, $30, $40, or $60 on the App Store.
As Star Dream said, things can go downhill if mistakes are done.
Honestly.... I don't know if this would be totally a good idea in reality.