Treadle feeders start at $36.00, the ones with the spring loaded doors start at $65.00. Plus the shipping, so like so many things that pay for themselves sometimes it is hard to make the investment. So folks just spend more money on feed until they can do better. My dad's dad always said, "Son, poor people have poor ways." Been there and done that.
Sometimes chickens will kill mice so the feed will be safe during the day. On occasion a hen chokes on a mouse so that isn't the perfect solution, t rex laying hens. Rats, most chickens won't mess with them and the rats quickly learn to eat during the day as long as they have a safe travel path to and from the coop or they burrow under the coop.
Do this, despite all the warnings not to do so, count your chickens and divide the number by four. Ignore any roosters, they eat little. That gives the pounds of feed per day you should be feeding, about one quarter pound per laying hen per day. Now start tracking your feed use and figure out how much those rats are costing you. And know that it just gets worse not better. Spend a lot of time and effort trapping them out by switching traps or investing in one of the live traps, have the population down somewhat, six weeks later you are back where you started on the rat population and you have smarter rats that are less likely to be trapped. Ditto on the poison. Never ends plus you wind up poisoning their natural predators.
Rats truly suck.