exchange-activesyncgmailiphone
When you set up GMail on an iPhone normally, the delete icon in the mail app is replaced by an archive icon, as this is the most common action in GMail.
I changed my settings to configure GMail as an Exchange account, as I wanted to enable push email for this account. But this has changed the archive icon to a delete icon.
Is it possible to maintain the archive icon while it's set up as a Gmail account?
You need to enable the "Delete Email As Trash" setting through Google Sync. Google added this feature in 2012:
Now when you delete an email on your iOS device, it will be sent to the "Trash" folder instead of the "All Mail" folder in Gmail.
Note: This feature is only relevant if you’ve setup your Gmail account in iOS mail as a Microsoft Exchange account.
The Verge gave a good writeup recommending the Gmail App + CalDAV + CardDAV: http://www.theverge.com/2012/12/5/3732364/best-way-gmail-google-calendar-iphone-how-to
The Gmail app solves both downsides you mention above. For CardDAV, it does a 15 min fetch, which is plenty good enough for me, so I don't see lack of push as being a real problem.
Best Answer
I'm actually about to ask the opposite question, but the delete functionality in Exchange GMail archives the email and does not delete it.