It seems like it gets you far enough. A custom IMAP client can just not download anything locally (just grab the headers and cache content of anything you've read), plus UI niceties (click on header to navigate to page). IMAP allows you to use this reader on platforms where no friendly client exists yet.
Oh yeah, totally; by having to "download all the items" I meant on the server. Assuming your were importing feed to an IMAP server that you owned, and reading feeds with a standard IMAP mail client. (Sounds kludgey, but really did work better than 90% of solutions to date.)
But if you mean a provider providing IMAP access to RSS feeds, that could work great. I don't know how to deal with updated items, but there is probably a way, especially if you had a custom client for key platforms. And 2nd tier platforms could still use an IMAP mail client.
