Good sized rats just push up the lid on that Chinese made feeder Grandpa feeder and feed during the day. Look at their
Amazon reviews, tons of complaints.
Ditto on the other Chinese made versions of that feeder, they simply are not rat proof and the rats will simply feed during the day. Mice probably won't get in unless they enter while a chicken is using the feeder, and some chickens will happily kill smaller mice. Locking it at night is a good idea but doesn't really solve the problem.
Building a rat proof coop is essential if the Grandpa feeder has already been purchased. I've never understood why they don't upgrade the design after more than 20 years and make it actually rat proof. Making it in China allows them plenty of profit to fix the design flaws, but they seem to be unwilling to change anything, and while their manufacture might have resisted the temptation to sell to others there are plenty of clones that are just as good if not better than the Grandpa feeder at cheaper prices.
I had a customer that was an engineer at Ditch Witch. They sold one unit to China back in the early nineties as a "sample", expecting to get into their market. Instead the Chinese copied the ditch digger and sold it at half the price. LOL To compete they had to oursource a lot of manufacturing over there and that just meant the number of competing knock off ditch diggers exploded. Then when you know who, he that shall not be named on the BYC forum, raised the tariffs they were hammered from both ends. Taxed higher on the sub-components and steel they were sourcing from China and still competing in other countries with the Chinese knock offs.
But your coop is an excellent example of Howard E.'s step two in the three step rodent control methods. Far better than using poison and traps and it accommodates smaller breeds and younger pullets. A bit expensive though but you knew it was going to work so it was a good investment.