Great point about Twitter and FB not having the "I've seen this" flag (although they probably have this info for their "engagement metrics"), it keeps people addicted and returning. I remember being glued to Twitter during the Mumbai terror attack, but the way it was designed, it was an endless stream of the same info, repeated. And spam, since bots add trending hashtags to their junk messages. I guess it's like cable news' rolling coverage, but instead of the same info repeated every hour, we can now read the same thing every second...
How about implementing an RSS interface on top of the likes of Twitter and Facebook by screen scraping? Would have to take authentication of course. Then we could consume it via RSS readers just like the good ol' days. Does that already exist? I would pay for that.
There is a tool that converts Twitter to RSS. I used to use it to get updates from a fantasy author who had neither a website nor a mailing list. It was self hosted but can't remember the name.