It's more to do with efficiency and one-to-many relationships. If op posts an archive link, only one person (op) has to lookup the link. Everyone else benefits.
Otherwise hundreds or thousands of readers have to individually look up the non paywalled link, or more likely, just skip the article altogether. So if you want to nudge people to read the article, why not just take a brief moment to reduce the effort required, and the article more accessible?
It's hardly a big ask, and I really don't see any good reason for the pushback. Ops time is so valuable they can't spare 30 seconds to get an archive link, but they expect the readers to each take that time?