None of these are easier than a cat to care for and none outcompete for cuteness. Bunnies are close to as cute but part of being cute for pets is also being intelligent, curious, and playful, which cats outcompete bunnies on. All of these things require cages that must be cleaned. Of the three only one of those animals can be safety potty trained, the bunny, and still it takes work to do it. A cat will use a litterbox almost instinctively. Most people don’t like owning birds majorly because of the need to clean the cage so much and that it feels cruel to cage a flying animal in general. Cleaning cages is at minimum a weekly exercise that is more work than simply scooping out soiled cat litter or just dumping out the whole bin of liter and replacing. Cages have to be washed and put back together in a manner the animal can actually live inside it. Additionally none of these can produce the same level of affection as a cat nor can be played with as easily or at all. You can train some birds to come to you, bunnies can be somewhat affectionate, neither of them match a cat. If you let a hamster out it will run away and unless you put in some serious training, probably never make it back to their cage because they are about the dumbest mammalian pet you can get.

This is not saying these are “bad” pets, but your question is why cat pictures are more prevalent than other pets and animals. This is why. They are superior pets as a whole based on those criteria. If this wasn’t the case and there was a more superior pet then that’s the pet that would prevail on the internet.