In addition to what Mary and others have said, there is a hidden danger with rats and mice. Fish and game agencies tell us that weasels, minks and the cousins dine almost exclusively on rodents.....like 95% plus of all they eat are rats, mice, gophers, moles, etc. And they also happen to be one of natures most vicious predators.....a good thing when they are after a colony of rats.
The danger lies in the potential of having a rat infestation attract a mink, weasel or one of the cousins to your coop. While they normally do not seek out chickens, if they do find them, they will easily make the transition to the birds and kill the entire flock in one attack. So a good thing when after rats, not so much when they are after your birds.
They are built not that much different from a rat and if a rat can get in, so can a weasel.
But to get rid of rats and mice is a tough job. It starts with starving them out, plus physically barring their entry and if those two are not enough, you may have to resort to poison to get rid of them. Yes.....a tough job to rid yourself of a rodent infestation.
On other hand, if you are willing to take a chance and also willing to accept it if your entire flock is wiped out, you could adopt a wait and see approach until you decide what you want to do.
If I had to guess, it would be that most folks who decide to give up their birds do so after the discovery of how many predators, rodents, parasites etc. are drawn to the birds and how big of a job it is to protect them. Most didn't bargain for that.