HTTP is used for a lot more than just web pages - as I mentioned above, it's a de facto standard for a great many internet applications that are not web-based. The benefits - well, Gabor Cselle summarizes these quite well (http://blog.gaborcselle.com/2010/02/how-to-replace-imap.html) - so many problems have already been solved with HTTP due to the massive interest in the web over the past 20 years.

But I take issue with the idea that replacing IMAP with HTTP would in any way upset the email infrastructure. Changing the client protocol does precisely nothing to the infrastructure, unless you choose also to replace SMTP completely. I could write my own server for my own email account, with HTTP for the client, and as long as it used SMTP to send and receive in the network, no-one would see any difference.