An actual paywall would be a lot less likely to work, because when people get to a paywall, they can't see what they're supposed to be buying, so they just go away and never come back. By contrast, this "works" because it gives people what they want unconditionally and then having accepted it without paying, guilts them into making a donation. Nonprofits have been running on this model forever.
But the real question is whether it's actually "working" -- the conversion rate to paid subscribers is evidently around 2%. That's pretty bad. And then they call it a success because it makes up 50% of their revenue instead of 20% as was traditionally true, but is that because subscriptions are up or because print advertising has been falling for so long? They only quote the most recent rate of change rather than the long-term numbers, and there may be one of these going on: [http://xkcd.com/605/]. When you first open a new revenue model, you can pretty well expect the first couple of years to have a higher growth rate than the ensuing years. Once everyone is subscribed who wants to subscribe, you have a hard time achieving any more subscription growth. And if subscriptions stop growing faster than advertising is falling, they're right back into the death spiral of cutting costs to save money which reduces readership which loses revenue which induces cost cutting.
The first segment consists of customers with a higher willingness to pay that aren't aware of the paywall workarounds or enjoy accessing the Times without futzing around. Who are these readers? Readers with high disposable income, older readers, and heavy readers.
The second segment consists of customers with a lower willingness to pay, who have identified the workarounds, and are willing to deal with the additional steps involved in bypassing the paywall. Who are these readers? Readers with lower disposable income, younger readers, and light readers.
The result of this segmentation is that the New York Times has been able to attract a significant number of online paying subscribers (segment 1), without decimating its overall readership figures (segment 1 + 2). By maintaining its overall readership figures, the New York Times has been able to preserve its online advertising revenue.
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[1] Since the product is nearly the same for both segments, aside from the steps involved in bypassing the paywall, you might consider this as an example of price discrimination.
And to everyone who objects "It's one step!", remember Step Zero:
Knowing it can be done.
Which implies Step Negative One:
Caring enough to find out.
It's hard to take those steps. There are, in point of fact, very likely a huge number of Steps Negative One you haven't yet taken, or are not going to take. I know that's true for me.
Were there worlds enough, and time, perhaps, but not as long as I'm living on the fourscore and ten plus change.
I also keep a rather extensive blocklist of URL-patterns I don't need my browser to load, ever. It took quite a while before I noticed (on a friend's computer, about 1.5y ago) that YouTube makes you watch ads before a video. I actually have no idea how that particular URL-pattern got into the blocklist, since I honestly hadn't seen those ads before. I suppose I was messing around with the webdev tool one day, noticed some resources that seemed unnecessary, I disabled them, videos continued to work fine, and forgot about it.
I realize this places me securely in the second segment, of course.