So do I.
But syncing mail with IMAP isn't good enough and many features of webmail clients do not map to IMAP clients. There are also tons of caveats during configuration so tons of people, rightfully so, don't bother.
IMAP is incredibly annoying. To send a message, you send via SMTP and then upload that message to your Sent folder, so it's transferred twice. For some reason the IMAP implementation I use means that when I move a message to a different folder, it uploads the message to the new folder, deletes the original message, and then downloads the message from the new folder. I have no idea if it's my server, client or the spec, but very wasteful and often fucks up.
Could you elaborate on this? I personally find using a mail client like Thunderbird to access my mail account far more responsive and seamless compared to using the webmail interface. If I don't have much bandwidth to work with, the local mail client using IMAP and SMTP will work while the webmail client will experience timeouts.