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Contacts is viewable through iTunes, would you not want that accessible through your computer?
Its in your contacts app and syncs the info to your phone.

Calendar is viewable through iTunes, would you not want that accessible through your computer?
Its in your iCal app and syncs the info to your phone.

Apple wrote the code for iTunes. iTunes already transfers settings, files, and code between X86 and ARM. Many of the iPhone access and settings are also already set in the X86 code and in ARM. It's something all of you already take for granted. It works already fine on both the iPhone & a computer. What's the problem understanding that?
Those apps are separate but are written to sync info. Even if Omni ran on both it would be two separate apps that sync your info, not one app that runs on both.

If it's just because it's hard, fine. I can understand that.
Many of these apps are written by developers who know how to code for the iPhone, but not the Mac/PC.

Although the question could be changed to: What's keeping a developer from doing what Apple has done, and have information that's appropriate to the application accessible through the computer?
Nothing, some apps do just that. I think Things does just that.
 
I'm pretty sure the OP's question was answered over a year ago. His question was worded incorrectly and confused many people. He wasn't really asking whether one could run iPhone apps on one's computer, but about third-party apps being able to sync with their iPhone clients. As has been noted, this is possible.

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