I just spent the last 15 minutes bringing myself up to speed on IMAP-IDLE. And I can see why Apple hasn't implemented it.
1) It requires an open TCP port to each server that you want to receive email from. This then requires one background thread for each of those ports. This creates a battery drain.
2) Since the TCP connection must stay open 24/7 that means it can't not be used on a WiFi connection to save power, unless they write code to handle the disconnect and reconnect scenario for each time the user switches mode. Hand off code like that is bound to fail especially when the users can cause the switch just by bringing the device out of sleep mode constantly.
I am not a developer so I cannot comment on the technicalities. I can, however, comment that, based on my own experience, imap idle is not a battery drain.
My old Nokia E71, running a Symbian OS and Profimail as an imap idle email client, would last more than my iphone 3gs and my Motorola Milestones running Android (I owned the Milestone 1 and 2, the European versions of the Droid). My Milestones, with the free imap idle email client k9-mail, last from one to two days depending on usage - keeping the apps I don't use, like facebook twitter etc disabled or uninstalled. This is a respectable battery life for a smartphone. My previous employer gave me an iphone 3gs with an Active Sync connection to my work email (Exchange server); well, with comparable usage I never got the iphone 3gs to last longer than my Nokia or my Motorola.
I have no clue if the IOS has some quirks that would cause imap idle to drain the battery; but I do know that I used imap idle on Nokias and Androids and it was no battery drain at all.
I think the push email system which requires the least battery usage is the Blackberry, because my understanding is (correct me if I'm missing something) that, when an email is received, the Blackberry server sends some sort of sms to the phone, prompting it to connect. However, blackberry plans are more expensive, and, last time I checked, the BIS doesn't sync the emails you delete or send from the phone; the BES does, but requires a usually very expensive data plan. I think BIS and BES stand for Blackberry Internet and Enterprise Server, or something like that. Not to mention the recent Blackberry debacle...
I would never use a smartphone which forces me to switch to an exchange or yahoo mail server to get push email. But clearly the success of the iphone suggests I am the minority...