What sort of current events do you want to find out about how quickly, and why?

You should consider, if you haven't already, the possibility that the value of learning about such things quickly is almost always almost exactly zero. Suppose e.g. there's an enormous earthquake half-way around the world from you, and many thousands of people die. That's a big deal, it's very important -- but what immediate difference should it make to your life?

One possibility: you might send a lot of money to a charity working in the affected place. But it seems unlikely to me that there's much real difference in practice between doing so on the day of the disaster and doing it a week later.

Another possibility (albeit a kinda callous one): it may come up in conversation and you may not want to sound bad. But I bet that in practice "social media, blogs, word of mouth or personal research" do just fine at keeping you sufficiently up to date that you don't sound stupid or ignorant. In any case, what you need to know about in order to sound up to date is probably roughly what you get from existing news sources, rather than from a hypothetical new source of genuinely important, sensibly prioritized news.