I think this became recommended practice in the days when usenet and email delivery was unreliable, bandwidth was expensive, and clients didn't have threaded interfaces or fold quoted sections. It's since been slavishly enforced on newcomers by groups that often have no idea of the original reasons for these protocols and why some may be no longer relevant.
Obviously sometimes it's most efficient to quote and interleave, when you want to reply to several points in a way that would be confusing without it. But with modern systems it's also fine to write a reply that doesn't make sense without the message it's in reply to, or a reply that quotes the whole message.
I've always read the advice as advice for readability. It's just text -- even in ancient times the bandwidth savings were not huge -- text does compress rather well.
[edit: This entire discussion is now at roughly 7K, or 3351 bytes after gzip (this is copy pasted, not the html) -- that's 89 seconds at 300 baud if I do the math correctly.
By comparison, my original reply was 166 bytes and compressed to 146 -- so would download in a fraction of a second. But note how poor the compression ratio is. Still doubt this was born out of a quest to save bandwidth (as most(?) were batch up/downloading discussion-lists at the time. And 300 baud is roughly typing speed -- that's a long time ago.]
It had more to do with the fact that you might be reading a reply to an original you hadn't seen yet, but which would be delivered to you in its entirety... soonish, for varying definitions of the word "soonish". And when I was a kid with 300 entire baud at my command, connection time actually cost money. (In '93, it wouldn't be uncommon for the access gateway to be long distance and charged per minute as well. Oh, Kansas City, how I miss thee not at all.)
Hm, well. I'm still not convinced the fact that you'd get the whole message anyway was very important. Even if you already have (instant) access to the previous mail -- I still much prefer reading a sanely typed/quoted reply. For example when arriving "late" to a discussion on a mailing list.
I don't exactly have fond memories (or more precisely my parents don't) of dialup (and later isdn) access -- we've never really had free local calls in Norway (and still don't). But since I was blasting away at 2400 baud, I was at least downloading faster-than-realtime (as in -- faster than you can read text).
Obviously sometimes it's most efficient to quote and interleave, when you want to reply to several points in a way that would be confusing without it. But with modern systems it's also fine to write a reply that doesn't make sense without the message it's in reply to, or a reply that quotes the whole message.