This has been the Business Plan of the Future for at least the last fifteen years. This Clay Shirky essay is getting on towards nine years old:
http://openp2p.com/pub/a/p2p/2000/12/19/micropayments.html
... and yet the counterexamples are still pretty thin on the ground. Where is the newspaper that thrives on micropayments? It's not like nobody has had the time to try it yet.
If the transaction is anything easier than a credit card transaction to process, it's not gonna be secure. There might be some attempt at some "no bother" microtransactions systems, until people start getting microbills from Kiev for 3,780,000 nickles for micro-porn. Ooops. I figure these microtrasaction system got about 6 months before Ukrainian hackers have figured out how to buy BMWs with nickles
Frankly, I think this approach is far worse than a flat subscription. And $0.25 is way to high. I would probably switch to a (lesser) news site that was free rather than pay a fee for 95% of the stuff out there.
Regardless, I don't think the random copies are that big of a deal. The only time something material is lost is when a copy gets posted to reddit or digg instead of the original. Few people are going to come across random copies of articles in obscure corners of the internet without direction.
Technically Google only index's top sites in near real time. CNN might be walked many times a day, but if you think that every blog or torrent site gets walked even close to a fraction as often then your mistaken.