If news subscriptions ever get around to working it has to happen the way things progressed with music: siloed content people mostly don't pay for (check), widespread piracy that allows people to enjoy unfettered access (let's say the Google trick/private browsing trick counts). Next comes the switcheroo phase, when a company comes along and makes heaps of illegal money off the piracy while negotiating with the content owners in a bid for legitimacy.
The economics are too hard otherwise. The New York Times won't cede pricing control willingly and consumers won't pay subscription prices to individual producers. And middleman companies will always have two impossible battles, pricing and content coverage.
Music might just be the sweet spot, though. Spotify works great while Netflix is getting torn apart by the sharks. Video might be too expensive/lucrative to aggregate and news articles might be too cheap/pervasive to bother.