"But I was always thinking of making iOS games and making their own hardware as mutually exclusive."
For Nintendo, it is. As far as I recall, Nintendo never released one its games on another platform. And Satoru Iwata (Nintendo's CEO) explained it lately [1]. Relevant quote:
"By integrating hardware and software, we can be unique. And because we have hardware and software developers in the same building, they stimulate each other."
Have you ever bought a Nintendo system just for its Nintendo games? I know I did. Several times. The N64 for Mario Kart and Mario 64, the GameCube for Mario Sunshine, the Wii for Mario Galaxy and Mario Kart again...
Maybe Nintendo looks like an idealist in a corporate-driven business, but consumers are somewhat sensible to Nintendo's commitment and that's why they're still successful.
It can backfire someday. Currently, the Wii U is sold at a loss [2]. I don't know how it will sort iself out. A bit too early to tell.
Anyway, Nintendo games on iOS would be hugely successful, but it's neither in their DNA nor in their long-term business strategy, no matter what gaming platform you're talking about (because yes, iOS has become a gaming platform).
[1] http://www.gamespot.com/news/iwata-explains-why-nintendo-won...
[2] http://www.gamespot.com/news/nintendo-continues-to-sell-wii-...