Why doesn't Flickr have a revenue model similar to YouTube based on views to share with users? Or even let you overlay links to other sites (advertising) on your photo?
Over at YouTube, users are willing to sit through 15 seconds of pre-roll ads so they can watch 3 minutes of whatever. Revenue is generated.
If a user arrives at Flickr, they've probably already found what they're looking for. Someone searching who arrives at a Flickr page of dolphins will see pictures of dolphins and have succeeded in their task. There's not much chance they'll notice any ads Flickr shows and click because they want NFL tickets.
I'm not saying Flickr should go down this road, but you're wrong in suggesting that sites can't make money from adverts unless they are pre-rolls or on search engines.