Not a strange reason but I will not start that discussion :p

I think Apple is currently fine with the position they have regarding mobile gaming having iOS as a platform/ecosystem for small games/apps. Maybe they will develop some mobile games but I doubt that. 

Of course! Who the hell wouldn't want to forget about that disaster of a console?

And because they failed once they would fail again? The Apple Newton wasn't such a success either, but they tried the PDA-concept a decade later again and combined it with an iPod and a phone and were quite successful with that smartphone.

~300 millions Game Center accounts and 13 billions US$ app-revenue last year (biggest share of the app-revenue = games) indicate that some people like to play on their iPhones and iPads.

A new Apple-TV with full game functionality and compatibility to already bought iOS-games would sell millions. You could connect a gamepad to it (over 300 iOS-games are already MFi-compatible, hundreds would follow) or an old iPod touch as input-device for touchscreen-only-games.

Don't for a second think that beacuse people "love to play on apple ipads/phones" that will in anyway translate to a successful HD home console console. The console hardware business is in no way easy, and it will make zero sense for apple to spend billions trying to get into a market that is already being torn between 3 active players. As it stands, if apple were to make a console tofday it would be very similar to whats already on offer by everyone else so all they will have to differentiate themselves are games which means studios. Truth is, apple stands a better chance cashing in on the game business is=f they just become a game publisher and fund and make special apple multiplatform games. But even that isn't easy cause building a dev team isn't easy.

So that's why every new mobile game launches at Windows Phone and Windows RT first and iOS users have to wait. ;)

No, but most of us want to.

Of course we forget just like how we forget Zelda CDI or Mario Hotel

I don't think that Apple is even interested to offer a high end console (which competes with PS4, XBO, Steamboxes and AIO-PCs connected to the TV)... that market is not profitable enough for them. They will probably not buy or build their own game studios and pump hundreds of millions in exclusive AAA-titles.

But eventually they have to offer an alternative to cheap Android consoles and the Vita-TV... by upgrading their (already successful) Apple-TV with an 64bit A7- or A8-SoC and adding iOS-game-functionality they could do that.

yea, but things could change if they release something like Amazon Fire TV. Their gaming market has grown tremendously since Pippen

That's because you go where the money is. PS2 got more games than Xbox, but the latter was way easier to develop for. If you develop and use all the SDKs, the iOS one is simply archaic compared to the Android one. You can do much more. I'm not talking about Bluetooth only, things like machine learning are simple on Android. Even design is simpler with good support to scalable design. All the updates that were needed to support the iPad when it was out can be handled in Android XML layout files easily with scalable layouts, autodetection of screen sizes and other easy things. Actually, only in Android you can do things that are really equivalent to a desktop OS.

About WP, its tools are really good. The overall SDK lacks a lot of things (the Android tools are lacking), but Visual Studio simply nails it. XCode is a joke compared to it. Debuging with Intellitrace is a complete new level. Other debugging tools are like riding a horse compared to drive a sports car. The design tools for WP (based on the former Blend Studio that is now integrated to VS) really make iOS and Android tools look amateurish.

In the end, you have Android with the best SDK and OS resources and WP with the best tools for development and design. iOS is behind in both aspects. If the three simply generated the same revenue (I'm talking more about WP, since Android is closing up by sheer numbers), WP would get heavy support.