While the real mail app will fetch mail automatically, it totally ignores your settings for how often to do it once the system's been idle for a couple minutes. As well, the iPhone mail app sucks in many other ways, such as not having filters, not being able to setup mail folders without doing it with some computer mail program and then syncing, not able to mark a mail read without reading it, etc. The iPhone mail app was obviously designed as an add-on to the Mac mail program and Microsoft Outlook, not as a stand-alone mail app.
I would kill for a real email app on the iPhone.