Most major news sites, as well as some other sites of reading content like Medium, have a paywall for certain articles, but those are easily defeated by people who bother to search the internet.
As I suspect said companies are aware of that, and they don’t react to properly protect their paid stuff, what do they expect to gain?
If you use a middleman such as archive.is it’s not their bandwidth anymore but the middleman’s. In most cases these services don’t act as a proxy but store a backup of the article on their servers. Not sure if that’s always the case though.