This situation is really annoying and needs to be fixed! The best (but annoying and a pain to set up) solution I've found is the following:
1. I sort my IMAP mail into folders as it comes in by creating rules at my ISP's email location (log onto my Control Center, go to the email account, and start creating rules).
2. Each rule that redirects an email into a subfolder copies it to the subfolder, leaving the original in my Inbox. A final catchall rule copies any mail not sorted into a subfolder into another subfolder I title "Unsorted". This is necessary so ALL mail is copied to a subfolder as well as ALL mail being in the Inbox.
3. On my PC I use Outlook (2010) without any Outlook rules and it downloads my ISP mail into the folders as sorted at my ISP using the ISP rules. This means Outlook doesn't need to be running to do the sorting, it's already sorted the moment it comes into the ISP's server. If you sort the mail in Outlook but don't have it running and open the iPhone, mail downloads into the Inbox and bypasses the filters.
4. On my ipad and iphone all my mail is in the Inbox, so I can monitor just the inbox for new and unread mail. iOS Mail does this well, which isn't saying much.
5. Back on Outlook I set up Auto Archive to delete Inbox mail (not the subfolders!) older than about 10 days, this way my ios devices don't get clogged with more than 10 days' of mail. If I need to access something older via ios I can look through the subfolders manually.
6. Still in Outlook I create two Search folders, one for all unread mail in all folders EXCEPT the Inbox, and another for ALL mail EXCEPT in the Inbox. I add these two folders to Favorites and most of the time in Outlook I use these two folders to monitor my recent mail and my unread mail. The Inbox is really there only for use on ipad/iphone.
7. Collateral Damage: a) this bloats the mailbox because mail is duplicated in the Inbox and subfolders, at least the recent mail is in Inbox until AutoArchive cleans it out. b) if I mark mail read on iPhone/iPod (inbox) it appears unread in my Outlook favorites folders (because they're seeing the mail in the subfolders not the Inbox), and vice versa. So I often find myself marking mail as read twice or deleting it twice.
I wish there were an alternate ios mail app that would display (1) all recent mail across all folders and Inbox and display in one list/folder/etc., and that would display (2) all UNread mail across all folders and Inbox in one list/folder/etc. If that day ever arrives, I can use my Inbox for unsorted mail and only move (not copy) the subfolder mail to the intended subfolders, as God meant IMAP to be used.
Awkward as my workaround is, the only alternative I can think of is to stop using subfolders, and I refuse to dumb down my desktop mail setup just to match the limitations of ios Mail. Would love to hear of a better solution!!!