I was one of a handful of people who wrote AIM bots for things like store-and-forward messaging. You tell the bot who you want to talk to and your message, and when they came back online the bot would send them your message. This completed the functionality we all needed: just make sure my message gets to the person eventually.
I don't think we want to bring back that experience. Facebook and WhatsApp and other messengers already give the ability to send a message when someone is offline, as well as letting you have a live interaction when online. All someone needs to do is set themselves as 'offline' and they can still get messages without having to respond. I think this is the right balance. The away message only makes sense if you want to be online and simultaneously tell people you aren't responding. Well, if you're not responding, why not just set yourself as offline?
However, I do like the idea of the away message as a polite OOO message. "Hello, I'm in the Adirondacks this weekend, I won't be back in contact until Monday." In this way you can politely tell friends why you're not responding and when they can try again.