The second diagram shows how the situation would look like if we'd manage to get over the idea that information is free. All content has to be produced somewhere by somebody and that somebody needs to live from something. It would make more sense to directly pay for news because the feedback loop isn't distorted by product sales. If you cut out the marketing here, you cut yourself off information about products and services, which would lead to incentives for more sensible advertisement rather than to incentives for more traffic-generating content aggregation.
Most providers of online news actually represent a mixture of these two cases, but the first case has become very dominant within the last decade or so. During the last years there has been a trend to subscriptions for online content, notably realized by the NYT paywall. Now the NYT is a very prominent newspaper with a large readership, and that it seems to be working for them doesn't mean it will be working for everybody. The problem is that the subscribers still pay, implicitly, for the advertisement cost with purchase of products. As long as there are news financed entirely or to a large extent by adverts, capitalism predicts people will prefer them (unless they are of considerably worse quality that is), and it will be very difficult for pay-for-content news providers to generate enough revenue.