I choose to feed mice to my chickens. They will eat mice anyway if they can catch them, just like they eat frogs or small snakes they catch. I don’t insist that anyone else feed mice to their chickens. I do not insist that no one feed mice to their chickens. It’s a personal choice.
If you...
They can jump really well but no, they cannot climb a smooth side. I store mfeed in a metal garbage can with a fairly tight fitting lid. It keeps possums and raccoons out too, not just mice and rats.
Here is my mouse trap that uses the principle they cannot climb something with really smooth...