(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.
I have just discovered that our cat likes icecream. As regards chasing mice he is a pacifist. The other day he was seen lying in our garden with a dormouse nibbling a fallen apple about 30cm from his nose.
My cat presented me with a very much alive and wriggling mouse yesterday. It was a great big ferocious critter, probably weighing well over a quarter of an ounce.
Well, I managed to catch it, then popped it in a cardboard box for an hour or so to give it a chance to calm down, then let it go, ready for the cat to catch at some other time.