Hmm. I use IMAP for desktop and mobile access - I have a web gateway available but I like my mobile device mail client so I just use IMAP with it. I get tons of server based storage using IMAP (using 11GB right now on my server, google gives me 7GB+ for free, you can pay for more if you buy pro - there are backup programs that will target an IMAP folder if you really want). My inboxes are always synchronized across my laptop, my wife's laptop (my login), and my mobile phone (different operating systems but IMAP handles that super well). Also since my server supports IDLE I don't have the client constantly polling the server - the TCP connection stays hot.
I'm not saying there isn't good reason to use whatever it is you think is better (I'm guessing exchange protocol) but the reasons have little to do with shortcomings in IMAP as an email access protocol.
thanks for the chat,
ram