Mobile email is hard. Those old standard email protocols don't cut it. Now, if you're willing to hand over your IMAP or POP3 username and password to Microsoft or RIM, they'll be happy to run your private email through their servers to your phone.
Edit: What's with the down votes?
Is it because I said the Gmail iOS client is a piece of shit? Well, it really is unreliable and unusable garbage. If it wasn't then that's what we all would be using.
Is it because I said mobile email is hard? Well, it is. That's why everyone here is looking for a better mobile email client.
Is it because I said IMAP and POP3 don't cut it? There's never been a remotely decent mobile IMAP or POP3 client. If there was, that's what we'd all be using.
It's 2015. Email has been around for 30+ years and everyone uses it, yet it remains an unsolved problem for many people.
IMAP IDLE works fine for me. Mail notification within milliseconds of arrival.
What do you feel is broken?
Disclaimer: I'm a maintainer of Sup, which is born on the same idea that tags + good search is much better than folders.