I've always wondered if news publications got too greedy. If I'm the revenue director at these news publications, why would I want FB/Google to pay me directly

I've always wondered if news publications got too greedy. If I'm the revenue director at these news publications, why would I want FB/Google to pay me directly or don't show me at all? I'd want them to show my news snippets as much as possible and when the user decides to click, it sends them to a paywall on my website. Now that FB and Google are instead deprioritizing news, I get way fewer visit to my paywalls. It's just a conversion rate formula. It felt like news publications wanted to double dip. Pay me to show me on your feed AND send traffic to my paywalls. That felt a bit too greedy.