This is probably because we are thinking about this the wrong way. The news sites today are engineered to catch your attention. But the market rewards companies who keep it. The New Yorker, The Economist, and NYT come up again and again on this site and others as examples of "the only news source I pay for" because of their quality content. Simply put, they don't make you feel stupid when you read them.
The problem is the amount of attention required to keep someone's attention is much less than the amount required to catch it, which is why BuzzFeed exists. What do people usually read on their lunch breaks? HuffPo. Until that changes, the landscape will be what it is.
I'm extremely interested in how Aeon.co will make those choices. They manage to consistently produce interesting, relevant, long articles but have no ads (yet). In an interview from 2012[1], its cofounder says, "Our business model is to spend the first year or so investing significantly in the magazine in order to build up a strong following or community of interested people – readers, writers, artists and photographers. Once we have established that reach we will start to build opportunities for generating revenue. We are not sure what forms these will take and are watching closely how other publications are doing so – from micro-payments for articles, to higher levels of service for subscribers, live events, and online fora." This quote tells me that even those in the industry have no idea and everyone is still making it up as they go along.
[1]http://www.frostmagazine.com/2012/10/brigid-hains-on-the-lau...