A couple years ago I discussed it with some people from a newspaper I worked for, and the bottom line was that they don't see another way at the moment. I don't know for sure if they view any model other than a subscription as crazy because they don't understand it, or they think they'll make less money, but the basic idea at the moment seems to be to have a certain (not huge) number of loyal subscribers, people that basically open your page first thing in the morning.
Bray thinks they are wrong because he will never subscribe to everything, but I'm not so sure he is right either. Can a smaller newspaper really compete with the New York Times? If I can pick between a micropayment for a NYT article and a smaller regional paper, who will get my money? Subscriptions let the publishers keep their head above water, which is best they have for now.
The more I think about, the more I think the model of a newspaper in general is stuck in an era where you had to buy a physical good to read news. You buy a newspaper, you like it, you subscribe. It gets delivered to you to your house. This is no longer the case and I can read whatever I want from anywhere on the globe (and I do). Most likely we will need to lose what we have before we realize there is value in having a local newspaper. If there is.