The problem that needs solving is that I would be willing to pay the NYT on a per article basis, but subscribing to them in entirety isn't worth it for me.

Right. You aren't a NYT customer. Really, you aren't worth their bother.

I want an account that I can fill that allows me to pay for content on a per-article bases that includes a large variety of media outlets. I would also love the ability to tip extra for articles I really appreciated. An app like that could possibly increase the reach of serious journalism.

Well, how much would you pay? 'cuz if NYT.com is $7 a month, and you intend to read one article a month, they'd probably have to hit you for $1 an article to make it worth it, which makes you scream "larceny!"

People who subscribe to the NYT don't necessarily read it cover-to-cover. Their subscription is also subsidized heavily by ads. We're still staring squarely at the problem of value - most customers don't value the NYT (for example) as heavily as the NYT needs to be valued in order for a partial plan to make sense. That's why none have emerged.