Think of the current way as POP email and the new way (iMessage in the cloud) as IMAP email.
This!!
I waded through 8 pages of posts wondering if anyone would mention this. The only trouble is, knowing the difference between POP and IMAP is one of those techie/geeky things that too many people can't appreciate.
"Modern" mail services like Gmail, Yahoo, MSN/Hotmail/Outlook, and iCloud mail use IMAP (Internet Message Access Protocol), where all messaging activity is maintained by the service, so that all actions are synced across all devices accessing the mail account. (For those in the institutional world, Microsoft Exchange-based mail systems are the equivalent.) The mail service has made a commitment to providing server storage space in order to ensure that the account data will be available and synchronized across multiple devices, regardless of what happens to/on any one of those devices.
POP (Post Office Protocol) is a much older email protocol, where the assumption is that the server/ISP is NOT responsible for providing storage - the original design assumption was that, as soon as mail was collected by the end user, it would be deleted from the server. That became very awkward when people started having multiple devices accessing the same account. The default behavior is still "delete when collected" (vs. "leave on server"). That means the mail might be deleted from the server before it can be downloaded to other devices. The end-user has to be sure settings for the account are consistent on all devices, or messages begin to fall through the cracks. Sent messages are only archived on the device that sent the message.
From my perspective, Apple's choice to make iMessage a POP-style service rather than IMAP was short-sighted and economically motivated. They certainly understood the benefits/shortcomings of each approach - but the infrastructure costs of IMAP are much higher than POP. Apple was not yet the mega-rich organization it is today, and iCloud's predecessor, MobileMe, had failed as a paid service due to competition from Google.
Apple knew they had to go "free," and undoubtedly knew that monetization of iMessage (and iCloud) would take many years. Further, messaging turned out to be a much bigger "thing" than anybody could have thought, back at that time. Cellular providers were mostly charging ridiculously high per-text-message pricing, and most people were still texting from 12-key flip phone keyboards (or exchanging email on Blackberrys), so text messaging traffic was relatively light (AOL Instant Messenger was a PC-based phenomenon). People didn't get into the habit of text-rather-than-call (and Twitter didn't become a medium of mass communication) until those 25-cent texts went away. iMessage was one of the vectors of that change. It's about time its grown up.