Because I could then build the entire interface client-side in a browser?
Don't get me wrong, I'm not a webdev guy. I have no front end/fullstack experience. I'm a longterm sysadmin/DevOps person. But if you're a power user, you want control over your mail interface/workflow. In that case, all your mailserver should be doing is accepting email for you, storing and indexing it, and serving it via API to clients you're using. I like IMAP, but it doesn't easily support some Gmail conventions (multiple labels per message).
IMAP and SMTP could easily be condensed into an XML/JSON API that could be done over HTTPS; I'm not familiar enough with CalDAV to say that though.
I believe ops point was that any stable api would be preferable to: "Yeah, there's an api, but we refuse to document it, and we'll randomly depricate stuff if you try to use it to build something that isn't gmail". The team behind gmail is probably one of the best qualified to hammer out a working api for email of json (what we have + a bit of what we want + stability and versioning). No reason why they couldn't publish that as an RFC and let people implement a front end for dbmail or whatnot that spoke the same api.