Here's why:
1. It took 2-3 years and several revisions for the iPod to become the trendy juggernaut of the MP3 player market, but even the iPod was just a replacement for walkmans and discmans. Thus, it had a preexisting market gap to fill.
2. Nintendo has set themselves up to undertake a task in marketing which could very well be impossible: sell a console (which cannot be "revised" like the iPod was) with a weird name to people who never thought to buy a console ever before. Nintendo is trying to push into a market which doesn't even know Nintendo ever intended to offer them a product in the first place.
3. The iPod is HUGE in Japan. Apple in general is huge in Japan, in fact.
4. The Wii's online store could include iTunes and, thanks to the USB 2.0 connectors on the Wii, could easily connect to all manners of iPod.
5. Apple has established the market mindset which Nintendo is already seeking. Rather than try to do this all by their lonesome, Nintendo would have a MUCH easier time selling Wii's to existing iPod owners. In fact, pushing the Wii as an iPod accessory alone would work to Nintendo's benefit.
6. They have common enemies: Sony (MP3 players) and Microsoft (software).
7. The iPod double's as the Wii's storage medium, making it the ultimate memory card. Even the cheaper iPods offer 5-10GBs of storage space which you can take to friend's houses and such. Plus, no need to buy any other memory card for iPod owners.
They're almost the same market: the crowd that Apple sold the easy and convenient MP3 player to would be the same crowd Nintendo seeks to sell the console for the non-gamer. If the iPod helps establish the Wii up as a trend, then that $100 million Nintendo doesn't need to spend on advertising.
I think it'd be the smartest move they could make. They're already trying hard to emulate Apple. Why not step it up and enter into a mutually beneficial agreement with them?