I wonder if they will. Newspapers are 85% advertising and the revenues from those sources is huge. Limiting readership of their websites should impact their advertising dollars at some point as people refuse to pay to access their websites.
There is a growing trend by competitors seeking the advertising dollar to publish a daily news vehicle sprinkled with advertising. Most carry up to date headline news, the weather and some local news. It is free to boot.
One can turn on the TV or radio which we pay for and are subjected to countless ads as well.You can access the various TV stations and news organizations via the web and read or view the latest news.
Charging to access a newspapers website seems to be overkill.