There's also the fact that popular shows have more pictures made of them. They get more fan art, and you'll see more people post official art of it without looking it up yourself, so you'll obviously save more of them.
The only kinds of pictures you'll casually save while watching anime instead of saving from the internet are full unedited screenshots, and those are not posted unless a character said something funny that's relevant to the discussion or you're discussing cool looking shots. The kinds of images that tend to be posted more often tend to be edited in some way (reaction images tend to be cropped for example). Since they require more effort than just clicking the s key on your keyboard, people get them from the internet rather than make them themselves while watching the anime, so the amount of such images from a particular anime is directly proportional to its popularity.