It would be incredibly bold for a major subscription content vendor, such as the NYTimes, to set up such a program. You sign into your NYTimes account, and sites around the web either become available to you, hide their advertising for you, or offer extra premium content just for NYTimes subscribers.

Basically, the app store model built upon the NYTimes, where you get the basic news from the New York Times and the niche stuff from content partners who the NYTimes will reimburse for page views, out of the subscription fee they are already collecting.

This would be so bold that I doubt it will happen from an existing print content vendor like NYTimes. Seems like something Amazon might do as a Prime benefit, though. Basically like Prime video, just for text.