Then you really don't understand how Apple works as a company. Nor Nintendo.
If Apple wants to ever get serious about gaming they are going to need to:
A) Encourage higher pricing / "premium" games to alter the economics of the App Store.
B) Focus more on innovative control input methods than just touch (as it exists now).
C) Have a box in the home that's more powerful than the current TV, with something that will encourage consumers and the industry to want to be a part of it.
To do these they would need to set a precedent by launching a new box/console with a stable mix of family friendly and some more core gamer friendly IP. Ones that people would be willing to pay for because of their reputation for quality and general brand recognition. This also provides them with more market differentiation from Android and Windows
Does that sound familiar to anyone? Who could provide them with that?
Nintendo.
Nintendo are a well known family oriented company with multiple family friendly and some hardcore IP with recognition that no other company will be able to match for many years.
For Nintendo, they are getting squeezed on both ends by continual advancements in mobile (as well as the race to the bottom for casual gaming), and at the high end by Sony / MS / PC. Although they might be able to do something great with whatever they have planned in NX, that market that propelled the Wii and the DS variants is unlikely to ever hit the same numbers again due to differences in the market.
Phones and other mobile devices offer more functionality and better software / connectivity, OSes, account systems, UI, etc etc etc than anything Nintendo can currently offer.
So what are Nintendo's options?
Try to negate mobile's advantages by making a phone?
— Do they make their own OS?
This is a terrible idea, and if Palm (WebOS), Microsoft (WP), Samsung (Tizen), can't get traction, what hope do Nintendo have?
— Do they adapt another OS?
This is also another terrible idea. They would more than likely end up using some variant of Android like Amazon do (FireOS). Can you imagine what the piracy levels will be once someone (inevitably) figures out a way to port/run Nintendo-android games on regular Android?
— Do they go full third party and just make games for everything?
This opens them up to the vast support headaches of different configurations of hardware for Android devices alone, never mind also supporting iOS and consoles.
Nintendo are a company that has long understood the value of software designed around the hardware and the value of having their IP be exclusive to their platform. It's not just a business decision but a mantra / ethos that the company lives by. They have always been strongly independent and could only ever truly partner with another company that understands those values.
Does that sound familiar to anyone? Who could provide them with that?
Apple.
Apple can provide them with a better system OS to build their games on, on cutting edge mobile hardware and software designed around it. By only designing for one platform and relatively fixed sets of hardware, they can allow for the lowered support requirements and optimisation they wouldn't be able to get if they made games for everything. Remaining as a first-party only studio also allows them to maintain the exclusivity of their IP's that helps them retain their value. They also no longer need to worry about competition from mobile when they are making games for hardware that does iPhone numbers. An addressable market MS and Sony would kill for (and are attempting to induce with the move to incremental hardware releases).
A lot of work would need to go into the merger. I'm not saying would all be perfect, but there is potential for both sides to gain as a single company. Apple could buy Nintendo and they remain "Nintendo" (getting rid of the brand is a mistake), they make games for a single platform (iOS/tvOS) and gain all of the benefits of mobile and a stronger OS foundation. While Apple gains legitimacy in the home/gaming space with a set of world class IP that matches their own product values.
But anyway, like I said, I don't really think it would ever happen.
If the market shares, the attach rates were more even I would agree, but I feel like the reality is for the majority of gamers is Nintendo having little to no effect on their gaming experience - most people can't, or won't buy multiple systems.
I think only two platforms is too few (it would end up like mobile where there is iOS and android and that's kinda it. I personally don't believe a duopoly is healthy for the industry long-term).
And yeh most people won't buy multiple systems, but they'll buy a Phone, TV and gaming system. So Nintendo may eventually have to secure themselves in one of those 3