The kind of smartphone screen displays that will work well for human visitors are not easily derived from web pages rendered on a desktop monitor. The only way of providing smartphone screen displays that work well is to develop Apps for the particular smartphone application.
Below are two Apps that work well on an Android smartphone. On the left is the initial display for Google Plus. On the right is the App for online banking with the Royal Bank of Canada. In both cases, tasks to be accomplished are very much easier in the App than in the equivalent mobile website.
Most of the news sources mentioned above also have Apps. They are often not visible enough on the main website but with a little searching, they usually can be found. One should not assume that all Apps will be designed well and will deliver an optimal visitor experience. However the odds are much higher and many of them do an excellent job of making online information readily available.
The One Web Principle has influenced much of the development of online websites in recent years. Many develop websites that work well on desktop PCs and then consider how to modify these to make them mobile friendly. The technical challenge involved is significant and yet the final result will rarely provide the simple interfaces that swiping fingers on small screens must have. It is much better to accept that the flexibility of designing an App for the particular source and for the specific mobile device will always result in a more satisfactory experience for the mobile visitor.