I found a partial solution for gmail accounts.
Follow this howto:
http://www.cnet.com/how-to/receive-push-gmail-alerts-on-ios-after-losing-actives ync-support/
After adding a "non-public" iCloud account, I couldn't find an easy way to limit the days of emails shown on the iPhone but at least if you seriously never share your icloud account you can routinely delete all emails from the icloud mailbox without any change to the way you handle your "real" gmail account.
Pros:
- it is a step in the right direction
- it gives you back push email with the native app with gmail
- it allows you to keep storage low on your iphone w/o changing your gmail behaviour
Cons:
- you need to manually purge icloud to keep storage use low on iphone
- when you flag an email in the native app, you don't flag it in gmail
The last point is what made me realise this workaround is not good enough for me, but maybe this is useful information to someone else.
good luck!