There are some great answers here already, I'll just add a what I think is different perspective on it.

Each newspaper is already charging you $0.01 an article, from their perspective. They give you an issue every day that has 100s of articles and it costs you like, a $1? $2? So each article is indeed super cheap for you to consume.

As others observe, you as a consumer probably aren't asking to be gated at every article - you are probably imagining some sort of general fund from which the paper draws down. Now if you really like just one paper or magazine, then you are back to a subscription model in this case.

So your use case is most probably that you want to read a FEW articles from LOTS of sites. Like, 20 from the NYT, 20 from WSJ, 30 from Slate etc.

Now the problem is to have an entity that is a 3rd party relative to these sites, which manages the common kitty. I vaguely remember some companies trying this, I can't remmeber the names, but you can see why this won't be easy. First, there's conflict of interest. It's tough to decide to enable a platform which also enables subscriptions to competing sources. Second, the platform company itself has to strike these deals individually because AT&T/the Mercers/George Soros haven't yet bought up all the news sources, which is a lot of friction.

And third, the execs at the sites have to decide that this complicated arrangement is really going to attract a completely new set of subscribers who actually like their content but just haven't signed up because the subscription price is too much. Why is it intuitive that _at scale_, a non subscriber's main barrier is not their affinity to or interest in the content itself, but this reluctance to commit to the subscription model? Why even should I assume that this unserved market has significant marginal utility to me as a company, relative to all the other ways I am making money? Even if all this is true, as an exec, I'd probably first experiment with tiered subscription on my site, and have multiple gates, rather than buy into some micro payment kitty system.

[Edit] As I ruminated on my own analysis, I realized that what you are looking for is the "cable TV" business equivalent for news sites. So maybe it's not totally undoable, if it's already happened with another media industry, but I think it'll be worth thinking about whether such a model works on time sensitive content or not. The typical participant in a cable TV system has a TON of resale value but with news articles, it's mostly one-and-done. Is there really enough aggregation value that a new business can survive on it? Just how many different versions of this riot and that election and those chicken fajita recipes and these 50 cool ways to decorate your bathroom are you, the consumer, going to pay for?

It could work if you started with some long-form subset of this content, and I think that's somewhat the inspiration behind sites like Medium and Substack. Not entirely ofc, because they are betting on the long tail of producers, not consumers, but there's also the aspect of the latter, in that this content tends to have long-term value.

As with any new business idea, there's no "will work/won't work" answer here. It's more like, "What form does this work in?"