Look at the 2.5 hour Facebook outage from a couple of days ago. If Facebook were to be hit by an airplane or asteroid, a seriously significant portion of 500,000,000 peoples' lives would be lost, if only just in photos. If my house were to have the same thing happen, 150 people would experience a somewhat lesser loss.
I have thousands of emails between close friends in Gmail that I would like to preserve, but no convenient system exists for archiving them away from Google. The point of archive is to have redundant systems on which to rely. Archiving my Gmail with Google is therefore not an archive since it's still only one system.
It's like leaving a tasty pork chop in the 'fridge at work and expecting the cleaning lady to not toss it over the weekend. I really think archive should be the responsibility of the user.
How about IMAP?
I haven't ran it in awhile but when I did it worked and was able to download my emails from the very beginning without crashing. Anyway, you might find it useful...
It would be very wise of Twitter to offer a bulk export function - not because they have to, but because it's to Twitter's benefit to not have me thinking twice about whether I should post to Twitter or communicate in some other, more archive-friendly way.