Solution: Install the Gmail app and it will send push notifications to you when you get new mails.
Thats what I do. I still use the stock mail app set to retrieve email hourly but also have the Gmail app installed to make sound when email arrives. A little delay waiting for the mail app to load is annoying but ok.
Keep in mind that the gmail app may have better abilities to download email in the background once IOS7 launches.
As for why Gmail doesn't do push, it's to give Android users a boost above iPhone users in functionality because google has an interest in encouraging Android.