I'm asking about the iPod (and not the iPhone) because I think there's general agreement that it is the best designed portable music player in the world. A poll asking this about the iPhone would no doubt lead to all kinds of tangents.
Hardware doesn't work like that, unless it's made of a handful of hand-soldered parts, and even then the results tend to be more functional than beautiful, and they suffer from lots of quality-control variation.
So, no. The best you can realistically hope for is for something like the Chumby: Designed by a core team, who sells it to defray the manufacturing and development costs but gives you all the schematics and software and encourages you to hack it.
Meanwhile, large companies have spent millions of dollars to compete with iPod and failed, so you're not exactly setting your sights low.
Steve Jobs often refers to iPod/iTunes as one of Apple's three "legs": http://www.macpredictions.com/2008/06/since-when-did-four-le...
They rely on producing a superior product/user experience/brand to dominate the market and as long as they stay good at that there is no reason to leave cash on the table.