I don’t think they are intentionally sifting through the feed. It is a crumb feed and every morsel is the same as the next. As they peck, crumbs go spraying after each strike of their beak into the feeder. When I muck out the coop after using a gravity feeder, there is feed on the floor under the feeder. I may go weeks without using the gravity feeder, then have to use it for a weekend away. Bang! The rodent buffet is back.
I have tried the no-waste bucket feeders and the waste was worse. They were kinda scooping out feed as they withdrew their heads. Other people swear by them .
I don’t expect I’ll ever eliminate every rodent. Every place I’ve known that had poultry, also had rodents. But I need to prevent it from getting to my neighbors’ apocalyptic level.