Skyring - sorry about the bad tech specs (trying to work too), but I think there's a big flaw in your logic. You're assuming an Apple handheld has to target the DS/PSP demographic.
Apple's strength has always be redefining the demographic - not taking markets, but CREATING markets. Look at the iPod and iPhone. People flocked to these devices in droves and they - technically speaking - really aren't the greatest in their traditional markets.
Most early iPod adopters hadn't bought a Rio, just as a large % of iPhone buyers had never owned a smart phone.
An Apple handheld would likely target an unidentified niche or seem rather than go head-to-head with conventional devices. At least that's my guess.
Apple didn't create shit with the iPod or iPhone. They went into a semi-establish (MP3 player) market or a well established one (smart phone) market. What have they done correctly in those? Claim innovation where there is little and in one case not make a stupid interface. Other than that they've often lacked features (To this day why someone would buy a iPod baffles me BEYOND BELIEF) and had a interface that really isn't any simpler than others in the iPod.
Apple I can see as a great marketing company, one of the best in fact. They make their products hip, make you want to own one. Make everyone else having one cool. Make you feel like you need one. They don't even pull punches there, their iPhone adds outright say you don't even need this device basically. Yet people buy them. The problem is their is a player who knows style, innovation, and mass market appeal in the handheld market: Nintendo. Nintendo has the cute little device, its cheap, it has a ton of games, and it has a neat feature in touch controls already. It's completely established, it's extremely simple to use. What is there for Apple to grab here? A device that's likely more expensive aimed at the casual players? It'll need to be cheaper than the DS (highly unlikely) or pack more features in a cheaper than PSP package (razor thin margin).
I'm trying real hard to think of the niche they could go for. They can only compete, not dominant, the marketing factor vs a DS. So that means they actually would have to create a niche this time and I just don't see it.
I disagree with that. If they're going after the 'casual' market a la Wii, they could go with something simplistic. You wouldn't even need 3D hardware to be able to support titles that many current iPod owners might be interested in playing. High quality AA'd 2D vector drawing would suffice for platformers and puzzlers and top-down racers and all sorts, like a SNES/Megadrive/Amiga in game offerings.
Cheaper than DS yet innovative and more feature filled? For a company that seems all about integration that doesn't seem much into Apple's typical strategy.