(Software) Cats shouldn't have milk too often but binge-licking every now and again won't do any harm. Cats are also useful for hoovering up bits of chicken off the floor.
Ours occasionally comes along and licks the milk at the bottom of our muesli bowls. And she's much better at dealing with the mice than the traps. She also spends a lot of time sitting on the internet, acting as some kind of firewall I think.
We've recently discovered that there are at least two other cats in the building, which could be why we saw a flurry of mouse activity before we got ours.