If I was a subscribed to something And the website showed me adds, I would simply write the website asking for the ads to be removed for paid users. If they did not remove the ads would unsubscribe. In your case of the local news paper you might even be able to take it the step further and put pressure on them to remove the ads by calling your local news stations tip line.
It should be illegal to steal access to something people put work into and in many cases live off the money that work makes.
Could you please explain how it's not stealing access to websites?
Because the site owner is not owed the revenue from ad impressions from its visitors. Where's the signed agreement that I have to watch X ads or earn the site owner Y dollars in ad revenue in exchange for viewing their articles?