4 out of 30 is actually not bad for cold asks. I usually see 10-20% depending on the site type. Bloggers and small review sites convert way better than news sites, news sites almost never edit old articles.
Thing that helped me: offer something that makes the edit worth it for them. A better product image, an updated spec, a correction if they got a price or detail wrong. ‘Link us please’ is a favour, ‘here’s a fix for your article’ is useful.
Still works but the response rates are way lower than the old case studies. I ran one earlier this year: about 300 emails, 11 links. That’s with personalised emails and a genuinely better replacement resource.
The good part is those 11 were real links on real resource pages, not stuff you pay for.