Anyone who has one or more pet pigeons can tell you that assuming that pigeons poop all over the place, non-stop, is just as ridiculous as assuming that humans poop all over the place, non-stop.
We are a mammal species.
We took pigeons from their (sub)tropical sea cliffs and spread them all over the world. Pigeons are immensely intelligent creatures. In many ways, they are smarter and more capable than humans.
In addition, birds have been on the planet immensely much longer than humans, and look what WE have done to the planet. Here are two must-watch documentaries: