I consider swipe to delete one of the best improvements ever to email. I guarantee that if you manage your email from your iPhone you will start to delete more email, and that alone will make you more productive. A lot of emails never need to be opened, especially since you can see the first line on your iPhone.
If you write shorter emails you will be more productive, if you manage email on your iPhone you will write shorter emails. This is true simply because of the nature of the medium change from a computer to a phone. With out a keyboard we don't want to write long emails, and our brains are already wired to write short and to the point messages while on our phones.
If you manage email from your iPhone you will actually get it done because you will be able to use the tiny inbetween times when you are not at your desk to do it. When you are waiting for a meeting to start, or you are in line, or your windows 8 computer decided it had to shut itself down right then, you will be able to get your email taken care of during these little times.
There it is, three reasons you should manage your email on your iPhone. And remember, live better.