Oh I'm sure there is something like that already in action. As one of many tools in the digital arsenal. But remember what OP was about. This thread was about whether or not the social media services should have a duty to report potential criminal behavior. That's just not workable. A robot in some NSA basement scanning Twitter relentlessly? Absolutely. Some kind of magic formula that immediately warns some techie in Frisco that it's time to call the cops? No way.
Computers know a lot more about us than people would be comfortable with if they really thought about it, but it's all brute force. Google knows which ads to serve you because it has years worth of your search history to tell it what you're interested in. The NSA robot above can compile a list of accounts that agents should keep an eye on, based on previous posting history, list of followers, etc. But what OP is hoping for here, sort of an early warning system based on a bare minimum of information, isn't going to work. In the past hour, 23 Twitter users have used the phrase "I will kill you" in a public post. Now multiply that by the number of phrases that you might need to put on your search list to be useful. You'll be swamped in very short order.
Now, if you combine the watch list from our NSA robot with a search list of worrisome phrases, that might result in a manageable number of serious red flags to look at, but it will still be almost entirely false positives, and the actual positives are only going to cover a minority of the people broadcasting future crimes online. It's still not going to catch the high school senior who snaps and shoots up the school, or the middle-aged guy who only uses social media to talk about sports, but found out last week his wife is cheating on him, and has decided to do something about it. The kid's "Today, everyone pays for what they did to me," and the man's "Time for the bitch to suffer" are likely not getting caught up in those filters, because the computer never had any reason to have those users on the watch list in the first place.