I think you have that the wrong way around. Archive services have to explicitly bypass paywalls so most local newspapers are simply unsupported.
The CMS usually allows search engines to get all content. The feature is to know human browser operators and make them pay, or know archiving/unblocking services and block them.
When previously nobody would have gone through the effort to build and maintain a custom scraper against a moving target, for some small to medium size city's newspaper, now it's just one of a myriad of 'scraper profiles' you can have a near fully automated tool create.